Mathematische Nachrichten最新文献

{"title":"A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains","authors":"Petteri Harjulehto,&nbsp;Peter Hästö,&nbsp;Artur Słabuszewski","doi":"10.1002/mana.202300416","DOIUrl":"https://doi.org/10.1002/mana.202300416","url":null,"abstract":"<p>Conditions for harmonic analysis in generalized Orlicz spaces have been studied over the past decade. One approach involves the generalized inverse of so-called weak <span></span><math>\u0000 <semantics>\u0000 <mi>Φ</mi>\u0000 <annotation>$Phi$</annotation>\u0000 </semantics></math>-functions. It featured prominently in the monograph <i>Orlicz Spaces and Generalized Orlicz Spaces</i>\u0000[P. Harjulehto and P. Hästö, Lecture Notes in Mathematics, vol. 2236, Springer, Cham, 2019]. While generally successful, the inverse function formulation of the decay condition (A2) in the monograph contains a flaw, which we explain and correct in this note. We also present some new results related to the conditions, including a more general result for the density of smooth functions.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300416","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142170078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regularity results for Hölder minimizers to functionals with non-standard growth","authors":"Antonio Giuseppe Grimaldi,&nbsp;Erica Ipocoana","doi":"10.1002/mana.202300412","DOIUrl":"10.1002/mana.202300412","url":null,"abstract":"<p>We study the regularity properties of Hölder continuous minimizers to non-autonomous functionals satisfying <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(p,q)$</annotation>\u0000 </semantics></math>-growth conditions, under Besov assumptions on the coefficients. In particular, we are able to prove higher integrability and higher differentiability results for solutions to our minimum problem.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Well-posedness and time decay of fractional Keller–Segel–Navier-Stokes equations in homogeneous Besov spaces","authors":"Ziwen Jiang,&nbsp;Lizhen Wang","doi":"10.1002/mana.202300325","DOIUrl":"10.1002/mana.202300325","url":null,"abstract":"<p>In this paper, we consider the parabolic–elliptic Keller–Segel system, which is coupled to the incompressible Navier–Stokes equations through transportation and friction. It is shown that when the system is diffused by Lévy motion, the well-posedness of the mild solution to the corresponding Cauchy problem in homogeneous Besov spaces is established by means of the Banach fixed point theorem. Furthermore, we prove the Lorentz regularity in time direction and the maximal regularity of solutions. In addition, we obtain the additional regularity and explore the time decay property of global mild solutions.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140968062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Hilbert-space variant of Geršgorin's circle theorem","authors":"Marcus Carlsson,&nbsp;Olof Rubin","doi":"10.1002/mana.202300153","DOIUrl":"10.1002/mana.202300153","url":null,"abstract":"<p>We provide a variant of Geršgorin's circle theorem, where the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>ℓ</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$ell ^1$</annotation>\u0000 </semantics></math>-estimates are swapped for <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>ℓ</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$ell ^2$</annotation>\u0000 </semantics></math>-estimates, more suitable for the infinite-dimensional Hilbert space setting.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300153","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140985550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hyperelliptic genus 3 curves with involutions and a Prym map","authors":"Paweł Borówka,&nbsp;Anatoli Shatsila","doi":"10.1002/mana.202300468","DOIUrl":"10.1002/mana.202300468","url":null,"abstract":"<p>We characterize genus 3 complex smooth hyperelliptic curves that admit two additional involutions as curves that can be built from five points in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$mathbb {P}^1$</annotation>\u0000 </semantics></math> with a distinguished triple. We are able to write down explicit equations for the curves and all their quotient curves. We show that, fixing one of the elliptic quotient curve, the Prym map becomes a 2:1 map and therefore the hyperelliptic Klein Prym map, constructed recently by the first author with A. Ortega, is also 2:1 in this case. As a by-product we show an explicit family of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>d</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(1,d)$</annotation>\u0000 </semantics></math> polarized abelian surfaces (for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$d&amp;gt;1$</annotation>\u0000 </semantics></math>), such that any surface in the family satisfying a certain explicit condition is abstractly non-isomorphic to its dual abelian surface.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141058686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global existence and stability of the wave equation with boundary variable damping","authors":"Boulmerka Imane,&nbsp;Hamchi Ilhem","doi":"10.1002/mana.202300003","DOIUrl":"10.1002/mana.202300003","url":null,"abstract":"<p>In this paper, we present the result of global existence of solution for the wave equation with boundary variable damping term. Then, we prove that this global solution is stable. Our study is based on the semi-groups theory and some integral inequalities.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The fundamental solution of the master equation for a jump-diffusion Ornstein–Uhlenbeck process","authors":"Olga S. Rozanova,&nbsp;Nikolai A. Krutov","doi":"10.1002/mana.202300200","DOIUrl":"10.1002/mana.202300200","url":null,"abstract":"<p>An integro-differential equation for the probability density of the generalized stochastic Ornstein–Uhlenbeck process with jump diffusion is considered for a special case of the Laplacian distribution of jumps. It is shown that for a certain ratio between the intensity of jumps and the speed of reversion, the fundamental solution can be found explicitly, as a finite sum. Alternatively, the fundamental solution can be represented as converging power series. The properties of this solution are investigated. The fundamental solution makes it possible to obtain explicit formulas for the density at each instant of time, which is important, for example, for testing numerical methods.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction to “Isomorphisms of Galois groups of number fields with restricted ramification”","authors":"","doi":"10.1002/mana.202480013","DOIUrl":"10.1002/mana.202480013","url":null,"abstract":"<p>R. Shimizu, <i>Isomorphisms of Galois groups of number fields with restricted ramification</i>, Math. Nachr. <b>296</b> (2023), 3026–3033. https://doi.org/10.1002/mana.202100438</p><p>References for this article are updated.</p><p>We apologize for this error.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202480013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linearization of holomorphic Lipschitz functions","authors":"Richard Aron,&nbsp;Verónica Dimant,&nbsp;Luis C. García-Lirola,&nbsp;Manuel Maestre","doi":"10.1002/mana.202300527","DOIUrl":"10.1002/mana.202300527","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math> be complex Banach spaces with <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mi>X</mi>\u0000 </msub>\u0000 <annotation>$B_X$</annotation>\u0000 </semantics></math> denoting the open unit ball of <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>. This paper studies various aspects of the <i>holomorphic Lipschitz space</i> <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mi>X</mi>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mi>Y</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathcal {H}L_0(B_X,Y)$</annotation>\u0000 </semantics></math>, endowed with the Lipschitz norm. This space consists of the functions in the intersection of the sets <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>Lip</mo>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mi>X</mi>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mi>Y</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$operatorname{Lip}_0(B_X,Y)$</annotation>\u0000 </semantics></math> of Lipschitz mappings and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mi>X</mi>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mi>Y</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathcal {H}^infty (B_X,Y)$</annotation>\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300527","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Periodic solutions of the parabolic–elliptic Keller–Segel system on whole spaces","authors":"Nguyen Thi Loan,&nbsp;Van Anh Nguyen Thi,&nbsp;Tran Van Thuy,&nbsp;Pham Truong Xuan","doi":"10.1002/mana.202300311","DOIUrl":"10.1002/mana.202300311","url":null,"abstract":"<p>In this paper, we investigate to the existence and uniqueness of periodic solutions for the parabolic–elliptic Keller–Segel system on whole spaces detailized by Euclidean space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mspace></mspace>\u0000 <mspace></mspace>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mspace></mspace>\u0000 <mtext>where</mtext>\u0000 <mspace></mspace>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>4</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathbb {R}^n,,(hbox{ where }n geqslant 4)$</annotation>\u0000 </semantics></math> and real hyperbolic space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mspace></mspace>\u0000 <mspace></mspace>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mtext>where</mtext>\u0000 <mspace></mspace>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathbb {H}^n,, (hbox{where }n geqslant 2)$</annotation>\u0000 </semantics></math>. We work in framework of critical spaces such as on weak-Lorentz space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mrow>\u0000 <mfrac>\u0000 <mi>n</mi>\u0000 <mn>2</mn>\u0000 </mfrac>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^{frac{n}{2},infty }(mathbb {R}^n)$</annotation>\u0000 </semantics></math> to obtain the results for the Keller–Segel system on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^n$</annotation>\u0000 </semantics></math> and on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mfrac>\u0000 <mi>p</mi>\u0000 <mn>2</mn>\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}