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A sharp multiplier theorem for solvable extensions of Heisenberg and related groups 海森堡群及相关群可解扩展的尖锐乘数定理
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-26 DOI: 10.1007/s10231-023-01405-z
Alessio Martini, Paweł Plewa
{"title":"A sharp multiplier theorem for solvable extensions of Heisenberg and related groups","authors":"Alessio Martini,&nbsp;Paweł Plewa","doi":"10.1007/s10231-023-01405-z","DOIUrl":"10.1007/s10231-023-01405-z","url":null,"abstract":"<div><p>Let <i>G</i> be the semidirect product <span>(N rtimes mathbb {R})</span>, where <i>N</i> is a stratified Lie group and <span>(mathbb {R})</span> acts on <i>N</i> via automorphic dilations. Homogeneous left-invariant sub-Laplacians on <i>N</i> and <span>(mathbb {R})</span> can be lifted to <i>G</i>, and their sum <span>(Delta )</span> is a left-invariant sub-Laplacian on <i>G</i>. In previous joint work of Ottazzi, Vallarino and the first-named author, a spectral multiplier theorem of Mihlin–Hörmander type was proved for <span>(Delta )</span>, showing that an operator of the form <span>(F(Delta ))</span> is of weak type (1, 1) and bounded on <span>(L^p(G))</span> for all <span>(p in (1,infty ))</span> provided <i>F</i> satisfies a scale-invariant smoothness condition of order <span>(s &gt; (Q+1)/2)</span>, where <i>Q</i> is the homogeneous dimension of <i>N</i>. Here we show that, if <i>N</i> is a group of Heisenberg type, or more generally a direct product of Métivier and abelian groups, then the smoothness condition can be pushed down to the sharp threshold <span>(s&gt;(d+1)/2)</span>, where <i>d</i> is the topological dimension of <i>N</i>. The proof is based on lifting to <i>G</i> weighted Plancherel estimates on <i>N</i> and exploits a relation between the functional calculi for <span>(Delta )</span> and analogous operators on semidirect extensions of Bessel–Kingman hypergroups.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 3","pages":"1361 - 1408"},"PeriodicalIF":1.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139053790","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 about the mean value property and some weighted Poincaré-type inequalities 关于均值性质和一些加权波恩卡莱式不等式的评论
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-24 DOI: 10.1007/s10231-023-01408-w
Giorgio Poggesi
{"title":"Remarks about the mean value property and some weighted Poincaré-type inequalities","authors":"Giorgio Poggesi","doi":"10.1007/s10231-023-01408-w","DOIUrl":"10.1007/s10231-023-01408-w","url":null,"abstract":"<div><p>We start providing a quantitative stability theorem for the rigidity of an overdetermined problem involving harmonic functions in a punctured domain. Our approach is inspired by and based on the proof of rigidity established in Enciso and Peralta-Salas (Nonlinear Anal 70(2):1080–1086, 2009), and reveals essential differences with respect to the stability results obtained in the literature for the classical overdetermined Serrin problem. Secondly, we provide new weighted Poincaré-type inequalities for vector fields. These are crucial tools for the study of the quantitative stability issue initiated in Poggesi (Soap bubbles and convex cones: optimal quantitative rigidity, 2022. arXiv:2211.09429) concerning a class of rigidity results involving mixed boundary value problems. Finally, we provide a mean value-type property and an associated weighted Poincaré-type inequality for harmonic functions in cones. A duality relation between this new mean value property and a partially overdetermined boundary value problem is discussed, providing an extension of a classical result obtained in Payne and Schaefer (Math Methods Appl Sci 11(6):805–819, 1989).</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 3","pages":"1443 - 1461"},"PeriodicalIF":1.0,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139350754","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
Holomorphic extension in holomorphic fiber bundles with (1, 0)-compactifiable fiber 具有(1, 0)可压缩纤维的全态纤维束中的全态扩展
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-23 DOI: 10.1007/s10231-023-01412-0
Sergey Feklistov
{"title":"Holomorphic extension in holomorphic fiber bundles with (1, 0)-compactifiable fiber","authors":"Sergey Feklistov","doi":"10.1007/s10231-023-01412-0","DOIUrl":"10.1007/s10231-023-01412-0","url":null,"abstract":"<div><p>We use the Leray spectral sequence for the sheaf cohomology groups with compact supports to obtain a vanishing result. The stalks of sheaves <span>(R^{bullet }phi _{!}mathcal {O})</span> for the structure sheaf <span>(mathcal {O})</span> on the total space of a holomorphic fiber bundle <span>(phi )</span> has canonical topology structures. Using the standard Čech argument we prove a density lemma for QDFS-topology on this stalks. In particular, we obtain a vanishing result for holomorphic fiber bundles with Stein fibers. Using Künnet formulas, properties of an inductive topology (with respect to the pair of spaces) on the stalks of the sheaf <span>(R^{1}phi _{!}mathcal {O})</span> and a cohomological criterion for the Hartogs phenomenon we obtain the main result on the Hartogs phenomenon for the total space of holomorphic fiber bundles with (1, 0)-compactifiable fibers.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1529 - 1552"},"PeriodicalIF":1.0,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881534","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 Cheeger constant as limit of Sobolev-type constants 作为索波列夫型常数极限的切格常数
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-21 DOI: 10.1007/s10231-023-01413-z
Grey Ercole
{"title":"The Cheeger constant as limit of Sobolev-type constants","authors":"Grey Ercole","doi":"10.1007/s10231-023-01413-z","DOIUrl":"10.1007/s10231-023-01413-z","url":null,"abstract":"<div><p>Let <span>(Omega )</span> be a bounded, smooth domain of <span>({mathbb {R}}^{N},)</span> <span>(Nge 2.)</span> For <span>(1&lt;p&lt;N)</span> and <span>(0&lt;q(p)&lt;p^{*}:=frac{Np}{N-p})</span>, let </p><div><div><span>$$begin{aligned} lambda _{p,q(p)}:=inf left{ int _{Omega }left| nabla uright| ^{p}textrm{d}x:uin W_{0}^{1,p}(Omega ) text {and} int _{Omega }left| uright| ^{q(p)}textrm{d}x=1right} . end{aligned}$$</span></div></div><p>We prove that if <span>(lim _{prightarrow 1^{+}}q(p)=1,)</span> then <span>(lim _{prightarrow 1^{+}}lambda _{p,q(p)}=h(Omega ))</span>, where <span>(h(Omega ))</span> denotes the Cheeger constant of <span>(Omega .)</span> Moreover, we study the behavior of the positive solutions <span>(w_{p,q(p)})</span> to the Lane–Emden equation <span>(-{text {div}} (left| nabla wright| ^{p-2}nabla w)=left| wright| ^{q-2}w,)</span> as <span>(prightarrow 1^{+}.)</span></p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1553 - 1567"},"PeriodicalIF":1.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139028702","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
Isoparametric functions and mean curvature in manifolds with Zermelo navigation 具有 Zermelo 导航的流形中的等参数函数和平均曲率
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-20 DOI: 10.1007/s10231-023-01402-2
Benigno Oliveira Alves, Patrícia Marçal
{"title":"Isoparametric functions and mean curvature in manifolds with Zermelo navigation","authors":"Benigno Oliveira Alves,&nbsp;Patrícia Marçal","doi":"10.1007/s10231-023-01402-2","DOIUrl":"10.1007/s10231-023-01402-2","url":null,"abstract":"<div><p>The generalized Zermelo navigation problem looks for the shortest time paths in an environment, modeled by a Finsler manifold (<i>M</i>, <i>F</i>), under the influence of wind or current, represented by a vector field <i>W</i>. The main objective of this paper is to investigate the relationship between the isoparametric functions on the manifold <i>M</i> with and without the presence of the vector field <i>W</i>. Our work generalizes results in (Dong and He in Differ Geom Appl 68:101581, 2020; He et al. in Acta Math Sinica Engl Ser 36:1049–1060, 2020; He et al. in Differ Geom Appl 84:101937, 2022; Ming et al. in Pub Math Debr 97:449–474, 2020; Xu et al. in Isoparametric hypersurfaces induced by navigation in Lorentz Finsler geometry, 2021). For the positive-definite cases, we also compare the mean curvatures in the manifold. Overall, we follow a coordinate-free approach.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 3","pages":"1285 - 1310"},"PeriodicalIF":1.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881513","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
Laminated Timoshenko beam without complementary dissipation 无补充耗散的层叠式季莫申科梁
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-19 DOI: 10.1007/s10231-023-01387-y
M. S. Alves, R. N. Monteiro
{"title":"Laminated Timoshenko beam without complementary dissipation","authors":"M. S. Alves,&nbsp;R. N. Monteiro","doi":"10.1007/s10231-023-01387-y","DOIUrl":"10.1007/s10231-023-01387-y","url":null,"abstract":"<div><p>In this study, the stability problem of a laminated beam with only structural damping is analyzed. The results obtained in this study improve the analysis of the problem by investigating stability without introducing additional dissipation. This is accomplished by considering only the usual assumption of equal wave velocities as the stability criterion.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 2","pages":"927 - 944"},"PeriodicalIF":1.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138960854","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
Stretched non-positive Weyl connections on solvable Lie groups 可解李群上的拉伸非正 Weyl 连接
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-14 DOI: 10.1007/s10231-023-01409-9
Maciej Bocheński, Piotr Jastrzȩbski, Aleksy Tralle
{"title":"Stretched non-positive Weyl connections on solvable Lie groups","authors":"Maciej Bocheński,&nbsp;Piotr Jastrzȩbski,&nbsp;Aleksy Tralle","doi":"10.1007/s10231-023-01409-9","DOIUrl":"10.1007/s10231-023-01409-9","url":null,"abstract":"<div><p>We determine the structure of solvable Lie groups endowed with invariant stretched non-positive Weyl connections and find classes of solvable Lie groups admitting and not admitting such connections. In dimension 4 we fully classify solvable Lie groups which admit invariant SNP Weyl connections.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 3","pages":"1463 - 1481"},"PeriodicalIF":1.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01409-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411712","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}
引用次数: 0
Non-integrally closed Kronecker function rings and integral domains with a unique minimal overring 非积分闭合克罗内克函数环和具有唯一最小重环的积分域
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-14 DOI: 10.1007/s10231-023-01410-2
Lorenzo Guerrieri, K. Alan Loper
{"title":"Non-integrally closed Kronecker function rings and integral domains with a unique minimal overring","authors":"Lorenzo Guerrieri,&nbsp;K. Alan Loper","doi":"10.1007/s10231-023-01410-2","DOIUrl":"10.1007/s10231-023-01410-2","url":null,"abstract":"<div><p>It is well-known that an integrally closed domain <i>D</i> can be expressed as the intersection of its valuation overrings but, if <i>D</i> is not a Prüfer domain, most of the valuation overrings of <i>D</i> cannot be seen as localizations of <i>D</i>. The Kronecker function ring of <i>D</i> is a classical construction of a Prüfer domain which is an overring of <i>D</i>[<i>t</i>], and its localizations at prime ideals are of the form <i>V</i>(<i>t</i>) where <i>V</i> runs through the valuation overrings of <i>D</i>. This fact can be generalized to arbitrary integral domains by expressing them as intersections of overrings which admit a unique minimal overring. In this article we first continue the study of rings admitting a unique minimal overring extending known results obtained in the 1970s and constructing examples where the integral closure is very far from being a valuation domain. Then we extend the definition of Kronecker function ring to the non-integrally closed setting by studying intersections of Nagata rings of the form <i>A</i>(<i>t</i>) for <i>A</i> an integral domain admitting a unique minimal overring.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1483 - 1511"},"PeriodicalIF":1.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01410-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411692","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}
引用次数: 0
Splitting type results for pseudoconvex domains and remarks on their Nebenhülle 伪凸域的分裂类型结果及其 Nebenhülle 评论
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-13 DOI: 10.1007/s10231-023-01406-y
Arkadiusz Lewandowski
{"title":"Splitting type results for pseudoconvex domains and remarks on their Nebenhülle","authors":"Arkadiusz Lewandowski","doi":"10.1007/s10231-023-01406-y","DOIUrl":"10.1007/s10231-023-01406-y","url":null,"abstract":"<div><p>We give a very general splitting type theorem for biholomorphic maps close to identity in the context of smoothly bounded pseudoconvex domains (Theorem 1.4). As a particular case, in the context of worm domains, we essentially reprove the splitting type result (Theorem 1.3) from Bracci et al. (Math Z 292:879–893, 2019) (by a different method). We also discuss some properties of the Nebenhülle of worm domains.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 3","pages":"1409 - 1417"},"PeriodicalIF":1.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01406-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139006140","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}
引用次数: 0
Existence, uniqueness and stability for a nonlinear problem arising from stratified arctic gyres 分层北极涡旋非线性问题的存在性、唯一性和稳定性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-12-12 DOI: 10.1007/s10231-023-01411-1
Qixing Ding, Fang-fang Liao, Sulei Wang
{"title":"Existence, uniqueness and stability for a nonlinear problem arising from stratified arctic gyres","authors":"Qixing Ding,&nbsp;Fang-fang Liao,&nbsp;Sulei Wang","doi":"10.1007/s10231-023-01411-1","DOIUrl":"10.1007/s10231-023-01411-1","url":null,"abstract":"<div><p>In this paper, we derive a nonlinear model for stratified arctic gyres, and prove several results on the existence, uniqueness and stability of solutions to such a model, by assuming suitable conditions for the vorticity function and the density function. The approach consists of deriving a suitable integral formulation for the problem and using fixed-point techniques.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 4","pages":"1513 - 1527"},"PeriodicalIF":1.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138580446","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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