Journal of the London Mathematical Society-Second Series最新文献

{"title":"Local cone multipliers and Cauchy–Szegö projections in bounded symmetric domains","authors":"Fernando Ballesta Yagüe,&nbsp;Gustavo Garrigós","doi":"10.1112/jlms.12986","DOIUrl":"https://doi.org/10.1112/jlms.12986","url":null,"abstract":"<p>We show that the cone multiplier satisfies local <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$L^p$</annotation>\u0000 </semantics></math>-<span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 <annotation>$L^q$</annotation>\u0000 </semantics></math> bounds only in the trivial range <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>⩽</mo>\u0000 <mi>q</mi>\u0000 <mo>⩽</mo>\u0000 <mn>2</mn>\u0000 <mo>⩽</mo>\u0000 <mi>p</mi>\u0000 <mo>⩽</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$1leqslant qleqslant 2leqslant pleqslant infty$</annotation>\u0000 </semantics></math>. To do so, we suitably adapt to this setting the proof of Fefferman for the ball multiplier. As a consequence we answer negatively a question by Békollé and Bonami, regarding the continuity from <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$L^prightarrow L^q$</annotation>\u0000 </semantics></math> of the Cauchy–Szegö projections associated with a class of bounded symmetric domains in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>${mathbb {C}}^n$</annotation>\u0000 </semantics></math> with rank <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$rgeqslant 2$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12986","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142174156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the modulus of continuity of solutions to nonlocal parabolic equations","authors":"Naian Liao","doi":"10.1112/jlms.12985","DOIUrl":"https://doi.org/10.1112/jlms.12985","url":null,"abstract":"<p>A general modulus of continuity is quantified for locally bounded, local, weak solutions to nonlocal parabolic equations, under a minimal tail condition. Hölder modulus of continuity is then deduced under a slightly stronger tail condition. These regularity estimates are demonstrated under the framework of nonlocal <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplacian with measurable kernels.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12985","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142160292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nijenhuis operators with a unity and \u0000 \u0000 F\u0000 $F$\u0000 -manifolds","authors":"Evgenii I. Antonov,&nbsp;Andrey Yu. Konyaev","doi":"10.1112/jlms.12983","DOIUrl":"https://doi.org/10.1112/jlms.12983","url":null,"abstract":"<p>The core object of this paper is a pair <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>L</mi>\u0000 <mo>,</mo>\u0000 <mi>e</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(L, e)$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> is a Nijenhuis operator and <span></span><math>\u0000 <semantics>\u0000 <mi>e</mi>\u0000 <annotation>$e$</annotation>\u0000 </semantics></math> is a vector field satisfying a specific Lie derivative condition, that is, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mi>e</mi>\u0000 </msub>\u0000 <mi>L</mi>\u0000 <mo>=</mo>\u0000 <mo>Id</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {L}_{e}L=operatorname{Id}$</annotation>\u0000 </semantics></math>. Our research unfolds in two parts. In the first part, we establish a splitting theorem for Nijenhuis operators with a unity, offering an effective reduction of their study to cases where <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> has either one real or two complex conjugate eigenvalues at a given point. We further provide the normal forms for <span></span><math>\u0000 <semantics>\u0000 <mi>gl</mi>\u0000 <annotation>$mathrm{gl}$</annotation>\u0000 </semantics></math>-regular Nijenhuis operators with a unity around algebraically generic points, along with seminormal forms for dimensions 2 and 3. In the second part, we establish the relationship between Nijenhuis operators with a unity and <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-manifolds. Specifically, we prove that the class of regular <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-manifolds coincides with the class of Nijenhuis manifolds with a cyclic unity. Extending our results from dimension 3, we reveal seminormal forms for corresponding <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-manifolds around singularities.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12983","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Valuative invariants for large classes of matroids","authors":"Luis Ferroni,&nbsp;Benjamin Schröter","doi":"10.1112/jlms.12984","DOIUrl":"https://doi.org/10.1112/jlms.12984","url":null,"abstract":"<p>We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a <i>stressed subset</i>. This framework provides a new combinatorial characterization of the class of (elementary) split matroids. Moreover, it permits to describe an explicit matroid subdivision of a hypersimplex, which, in turn, can be used to write down concrete formulas for the evaluations of any valuative invariant on these matroids. This shows that evaluations on these matroids depend solely on the behavior of the invariant on a tractable subclass of Schubert matroids. We address systematically the consequences of our approach for several invariants. They include the volume and Ehrhart polynomial of base polytopes, the Tutte polynomial, Kazhdan–Lusztig polynomials, the Whitney numbers of the first and second kinds, spectrum polynomials and a generalization of these by Denham, chain polynomials and Speyer's <span></span><math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math>-polynomials, as well as Chow rings of matroids and their Hilbert–Poincaré series. The flexibility of this setting allows us to give a unified explanation for several recent results regarding the listed invariants; furthermore, we emphasize it as a powerful computational tool to produce explicit data and concrete examples.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12984","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142152281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the intersection form of fillings","authors":"Zhengyi Zhou","doi":"10.1112/jlms.12981","DOIUrl":"https://doi.org/10.1112/jlms.12981","url":null,"abstract":"<p>We prove, by an ad hoc method, that exact fillings with vanishing rational first Chern class of flexibly fillable contact manifolds have unique integral intersection forms. We appeal to the special Reeb dynamics (stronger than ADC in [Lazarev, Geom. Funct. Anal. <b>30</b> (2020), no. 1, 188–254]) on the contact boundary, while a more systematic approach working for general ADC manifolds is developed independently by Eliashberg, Ganatra and Lazarev. We also discuss cases where the vanishing rational first Chern class assumption can be removed. We derive the uniqueness of diffeomorphism types of exact fillings of certain flexibly fillable contact manifolds and obstructions to contact embeddings, which are not necessarily exact.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142152222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Around the Gauss circle problem: Hardy's conjecture and the distribution of lattice points near circles","authors":"Stephen Lester,&nbsp;Igor Wigman","doi":"10.1112/jlms.12977","DOIUrl":"https://doi.org/10.1112/jlms.12977","url":null,"abstract":"<p>Hardy conjectured that the error term arising from approximating the number of lattice points lying in a radius-<span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math> disc by its area is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>O</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <mo>+</mo>\u0000 <mi>o</mi>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$O(R^{1/2+o(1)})$</annotation>\u0000 </semantics></math>. One source of support for this conjecture is a folklore heuristic that uses i.i.d. random variables to model the lattice points lying near the boundary and square root cancellation of sums of these random variables. We examine this heuristic by studying how these lattice points interact with one another and prove that their autocorrelation is determined in terms of a random model. Additionally, it is shown that lattice points near the boundary which are “well separated” behave independently. We also formulate a conjecture concerning the distribution of pairs of these lattice points.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12977","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142123045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Homotopy properties of the complex of frames of a unitary space","authors":"Kevin I. Piterman,&nbsp;Volkmar Welker","doi":"10.1112/jlms.12978","DOIUrl":"https://doi.org/10.1112/jlms.12978","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;annotation&gt;$V$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a finite-dimensional vector space equipped with a nondegenerate Hermitian form over a field &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathbb {K}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathcal {G}}(V)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be the graph with vertex set the one-dimensional nondegenerate subspaces of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;annotation&gt;$V$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and adjacency relation given by orthogonality. We give a complete description of when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathcal {G}}(V)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is connected in terms of the dimension of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;annotation&gt;$V$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and the size of the ground field &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathbb {K}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Furthermore, we prove that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;dim&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$dim (V) &amp;gt; 4$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, then the clique complex &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathcal {F}}(V)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathcal {G}}(V)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is simply connected. For finite fields &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathbb {K}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we also compute the eigenvalues of the adjacency matrix of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142050539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On finitely generated Engel branch groups","authors":"J. Moritz Petschick","doi":"10.1112/jlms.12980","DOIUrl":"https://doi.org/10.1112/jlms.12980","url":null,"abstract":"<p>We construct finitely generated Engel branch groups, answering a question of Fernández-Alcober, Noce and Tracey on the existence of such objects. In particular, the groups constructed are not nilpotent, yielding the second known class of examples of finitely generated non-nilpotent Engel groups following a construction by Golod from 1969. To do so, we exhibit groups acting on rooted trees with growing valency on which word lengths of elements are contracting very quickly under section maps. Our methods apply in principle to a wider class of iterated identities, of which the Engel words are a special case.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12980","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142050540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global classical solutions to a multidimensional radiation hydrodynamics model with symmetry and large initial data","authors":"Jing Wei,&nbsp;Minyi Zhang,&nbsp;Changjiang Zhu","doi":"10.1112/jlms.12973","DOIUrl":"https://doi.org/10.1112/jlms.12973","url":null,"abstract":"&lt;p&gt;As a first stage to study the global large solutions of the radiation hydrodynamics model with viscosity and thermal conductivity in the high-dimensional space, we study the problems in high dimensions with some symmetry, such as the spherically or cylindrically symmetric solutions. Specifically, we will study the global classical large solutions to the radiation hydrodynamics model with spherically or cylindrically symmetric initial data. The key point is to obtain the strict positive lower and upper bounds of the density &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ρ&lt;/mi&gt;\u0000 &lt;annotation&gt;$rho$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and the lower bound of the temperature &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;θ&lt;/mi&gt;\u0000 &lt;annotation&gt;$theta$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Compared with the Navier–Stokes equations, these estimates in the present paper are more complicated due to the influence of the radiation. To overcome the difficulties caused by the radiation, we construct a pointwise estimate between the radiative heat flux &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;annotation&gt;$q$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and the temperature &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;θ&lt;/mi&gt;\u0000 &lt;annotation&gt;$theta$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; by studying the boundary value problem of the corresponding ordinary differential equation. And we consider a general heat conductivity: &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;κ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ρ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;θ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;θ&lt;/mi&gt;\u0000 &lt;mi&gt;β&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$kappa (rho,theta)geqslant C(1+theta ^beta)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ρ&lt;/mi&gt;\u0000 &lt;mo&gt;⩽&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ρ&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$rho leqslant rho _+$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;; &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;κ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ρ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;θ&lt;/mi&gt;","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142045288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Almost sure bounds for a weighted Steinhaus random multiplicative function","authors":"Seth Hardy","doi":"10.1112/jlms.12979","DOIUrl":"https://doi.org/10.1112/jlms.12979","url":null,"abstract":"<p>We obtain almost sure bounds for the weighted sum <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>∑</mo>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩽</mo>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <msqrt>\u0000 <mi>n</mi>\u0000 </msqrt>\u0000 </mfrac>\u0000 </mrow>\u0000 <annotation>$sum _{n leqslant t} frac{f(n)}{sqrt {n}}$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$f(n)$</annotation>\u0000 </semantics></math> is a Steinhaus random multiplicative function. Specifically, we obtain the bounds predicted by exponentiating the law of the iterated logarithm, giving sharp upper and lower bounds.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12979","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142045289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}