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Hypoelliptic functional inequalities 次椭圆函数不等式
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-29 DOI: 10.1007/s00209-024-03493-w
Michael Ruzhansky, Nurgissa Yessirkegenov
{"title":"Hypoelliptic functional inequalities","authors":"Michael Ruzhansky, Nurgissa Yessirkegenov","doi":"10.1007/s00209-024-03493-w","DOIUrl":"https://doi.org/10.1007/s00209-024-03493-w","url":null,"abstract":"<p>In this paper we derive a variety of functional inequalities for general homogeneous invariant hypoelliptic differential operators on nilpotent Lie groups. The obtained inequalities include Hardy, Sobolev, Rellich, Hardy–Littllewood–Sobolev, Gagliardo–Nirenberg, Caffarelli–Kohn–Nirenberg and Heisenberg–Pauli–Weyl type uncertainty inequalities. Some of these estimates have been known in the case of the sub-Laplacians, however, for more general hypoelliptic operators almost all of them appear to be new as no approaches for obtaining such estimates have been available. The approach developed in this paper relies on establishing integral versions of Hardy inequalities on homogeneous Lie groups, for which we also find necessary and sufficient conditions for the weights for such inequalities to be true. Consequently, we link such integral Hardy inequalities to different hypoelliptic inequalities by using the Riesz and Bessel kernels associated to the described hypoelliptic operators.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140812226","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}
引用次数: 0
An example of an infinite amenable group with the ISR property 具有 ISR 特性的无限可化群示例
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-29 DOI: 10.1007/s00209-024-03495-8
Yongle Jiang, Xiaoyan Zhou
{"title":"An example of an infinite amenable group with the ISR property","authors":"Yongle Jiang, Xiaoyan Zhou","doi":"10.1007/s00209-024-03495-8","DOIUrl":"https://doi.org/10.1007/s00209-024-03495-8","url":null,"abstract":"<p>Let <i>G</i> be <span>(S_{mathbb {N}})</span>, the finitary permutation (i.e., permutations with finite support) group on the set of positive integers <span>(mathbb {N})</span>. We prove that <i>G</i> has the invariant von Neumann subalgebras rigidity (ISR, for short) property as introduced in Amrutam–Jiang’s work. More precisely, every <i>G</i>-invariant von Neumann subalgebra <span>(Psubseteq L(G))</span> is of the form <i>L</i>(<i>H</i>) for some normal subgroup <span>(Hlhd G)</span> and in this case, <span>(H={e}, A_{mathbb {N}})</span> or <i>G</i>, where <span>(A_{mathbb {N}})</span> denotes the finitary alternating group on <span>(mathbb {N})</span>, i.e., the subgroup of all even permutations in <span>(S_{mathbb {N}})</span>. This gives the first known example of an infinite amenable group with the ISR property.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140812212","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}
引用次数: 0
A unified approach to inequalities for K-functionals and moduli of smoothness K 函数和平滑模量不等式的统一方法
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-29 DOI: 10.1007/s00209-024-03484-x
Amiran Gogatishvili, Bohumír Opic, Sergey Tikhonov, Walter Trebels
{"title":"A unified approach to inequalities for K-functionals and moduli of smoothness","authors":"Amiran Gogatishvili, Bohumír Opic, Sergey Tikhonov, Walter Trebels","doi":"10.1007/s00209-024-03484-x","DOIUrl":"https://doi.org/10.1007/s00209-024-03484-x","url":null,"abstract":"<p>The paper provides a detailed study of crucial inequalities for smoothness and interpolation characteristics in rearrangement invariant Banach function spaces. We present a unified approach based on Holmstedt formulas to obtain these estimates. As examples, we derive new inequalities for moduli of smoothness and <i>K</i>-functionals in various Lorentz spaces.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811970","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}
引用次数: 0
The twisted 1-loop invariant and the Jacobian of Ptolemy varieties 托勒密变体的扭曲一环不变量和雅各布数
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-26 DOI: 10.1007/s00209-024-03491-y
Seokbeom Yoon
{"title":"The twisted 1-loop invariant and the Jacobian of Ptolemy varieties","authors":"Seokbeom Yoon","doi":"10.1007/s00209-024-03491-y","DOIUrl":"https://doi.org/10.1007/s00209-024-03491-y","url":null,"abstract":"<p>We reformulate the twisted 1-loop invariant in terms of Ptolemy coordinates. In addition, we prove that the twisted 1-loop invariant is equal to the adjoint twisted Alexander polynomial for all hyperbolic once-punctured torus bundles. This shows that the 1-loop conjecture proposed by Dimofte and Garoufalidis holds for all hyperbolic once-punctured torus bundles.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","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":"140798762","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}
引用次数: 0
On the dynamic asymptotic dimension of étale groupoids 论埃塔莱群集的动态渐近维度
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-26 DOI: 10.1007/s00209-024-03492-x
Christian Bönicke
{"title":"On the dynamic asymptotic dimension of étale groupoids","authors":"Christian Bönicke","doi":"10.1007/s00209-024-03492-x","DOIUrl":"https://doi.org/10.1007/s00209-024-03492-x","url":null,"abstract":"<p>We investigate the dynamic asymptotic dimension for étale groupoids introduced by Guentner, Willett and Yu. In particular, we establish several permanence properties, including estimates for products and unions of groupoids. We also establish invariance of the dynamic asymptotic dimension under Morita equivalence. In the second part of the article, we consider a canonical coarse structure on an étale groupoid, and compare the asymptotic dimension of the resulting coarse space with the dynamic asymptotic dimension of the underlying groupoid.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","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":"140798766","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}
引用次数: 0
A remark on a weighted version of Suita conjecture for higher derivatives 关于高导数加权版绥塔猜想的评论
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-26 DOI: 10.1007/s00209-024-03486-9
Qi’an Guan, Xun Sun, Zheng Yuan
{"title":"A remark on a weighted version of Suita conjecture for higher derivatives","authors":"Qi’an Guan, Xun Sun, Zheng Yuan","doi":"10.1007/s00209-024-03486-9","DOIUrl":"https://doi.org/10.1007/s00209-024-03486-9","url":null,"abstract":"<p>In this article, we consider the set of points for the holding of the equality in a weighted version of Suita conjecture for higher derivatives, and give relations between the set and the integer valued points of a class of harmonic functions (maybe multi-valued). For planar domains bounded by finite analytic closed curves, we give relations between the set and Dirichlet problem.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","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":"140798786","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}
引用次数: 0
On the Brauer groups of fibrations 论纤维的布劳尔群
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-26 DOI: 10.1007/s00209-024-03487-8
Yanshuai Qin
{"title":"On the Brauer groups of fibrations","authors":"Yanshuai Qin","doi":"10.1007/s00209-024-03487-8","DOIUrl":"https://doi.org/10.1007/s00209-024-03487-8","url":null,"abstract":"<p>Let <span>({mathcal {X}}rightarrow C)</span> be a flat <i>k</i>-morphism between smooth integral varieties over a finitely generated field <i>k</i> such that the generic fiber <i>X</i> is smooth, projective and geometrically connected. Assuming that <i>C</i> is a curve with function field <i>K</i>, we build a relation between the Tate-Shafarevich group of <span>(textrm{Pic}^0_{X/K})</span> and the geometric Brauer groups of <span>({mathcal {X}})</span> and <i>X</i>, generalizing a theorem of Artin and Grothendieck for fibered surfaces to higher relative dimensions.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","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":"140798763","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}
引用次数: 0
Remarks on the existence of minimal models of log canonical generalized pairs 关于对数典范广义对的最小模型存在性的评论
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-26 DOI: 10.1007/s00209-024-03489-6
Nikolaos Tsakanikas, Lingyao Xie
{"title":"Remarks on the existence of minimal models of log canonical generalized pairs","authors":"Nikolaos Tsakanikas, Lingyao Xie","doi":"10.1007/s00209-024-03489-6","DOIUrl":"https://doi.org/10.1007/s00209-024-03489-6","url":null,"abstract":"<p>Given an NQC log canonical generalized pair <span>((X,B+M))</span> whose underlying variety <i>X</i> is not necessarily <span>(mathbb {Q})</span>-factorial, we show that one may run a <span>((K_X+B+M))</span>-MMP with scaling of an ample divisor which terminates, provided that <span>((X,B+M))</span> has a minimal model in a weaker sense or that <span>(K_X+B+M)</span> is not pseudo-effective. We also prove the existence of minimal models of pseudo-effective NQC log canonical generalized pairs under various additional assumptions, for instance when the boundary contains an ample divisor.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","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":"140798783","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}
引用次数: 0
Intermediate dimensions under self-affine codings 自曲线编码下的中间尺寸
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-26 DOI: 10.1007/s00209-024-03490-z
Zhou Feng
{"title":"Intermediate dimensions under self-affine codings","authors":"Zhou Feng","doi":"10.1007/s00209-024-03490-z","DOIUrl":"https://doi.org/10.1007/s00209-024-03490-z","url":null,"abstract":"<p>Intermediate dimensions were recently introduced by Falconer et al. (Math Z 296:813–830, 2020) to interpolate between the Hausdorff and box-counting dimensions. In this paper, we show that for every subset <i>E</i> of the symbolic space, the intermediate dimensions of the projections of <i>E</i> under typical self-affine coding maps are constant and given by formulas in terms of capacities. Moreover, we extend the results to the generalized intermediate dimensions introduced by Banaji (Monatsh Math 202: 465–506, 2023) in several settings, including the orthogonal projections in Euclidean spaces and the images of fractional Brownian motions.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","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":"140811982","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}
引用次数: 0
On multipliers into martingale $$SL^infty $$ spaces for arbitrary filtrations 论任意滤波的马廷格尔 $$SL^infty$ 空间乘数
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-21 DOI: 10.1007/s00209-024-03494-9
Anton Tselishchev
{"title":"On multipliers into martingale $$SL^infty $$ spaces for arbitrary filtrations","authors":"Anton Tselishchev","doi":"10.1007/s00209-024-03494-9","DOIUrl":"https://doi.org/10.1007/s00209-024-03494-9","url":null,"abstract":"<p>In this paper we study the following problem: for a given bounded positive function <i>f</i> on a filtered probability space can we find another function (a multiplier) <i>m</i>, <span>(0le mle 1)</span>, such that the function <i>mf</i> is not “too small” but its square function is bounded? We explicitly show how to construct such multipliers for the usual martingale square function and for so-called conditional square function. Besides that, we show that for the usual square function more general statement can be obtained by application of a non-constructive abstract correction theorem by Kislyakov.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140636576","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}
引用次数: 0
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