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Geometric Hardy and Hardy–Sobolev inequalities on Heisenberg groups Heisenberg群上的几何Hardy和Hardy - sobolev不等式
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-11-17 DOI: 10.1142/s1664360720500162
Michael Ruzhansky, Bolys Sabitbek, D. Suragan
{"title":"Geometric Hardy and Hardy–Sobolev inequalities on Heisenberg groups","authors":"Michael Ruzhansky, Bolys Sabitbek, D. Suragan","doi":"10.1142/s1664360720500162","DOIUrl":"https://doi.org/10.1142/s1664360720500162","url":null,"abstract":"In this paper, we present geometric Hardy inequalities for the sub-Laplacian in half-spaces of stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant: [Formula: see text] which solves a conjecture in the paper [S. Larson, Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domain in the Heisenberg group, Bull. Math. Sci. 6 (2016) 335–352]. Here, [Formula: see text] is the angle function. Also, we obtain a version of the Hardy–Sobolev inequality in a half-space of the Heisenberg group: [Formula: see text] where [Formula: see text] is the Euclidean distance to the boundary, [Formula: see text], and [Formula: see text]. For [Formula: see text], this gives the Hardy–Sobolev–Maz’ya inequality on the Heisenberg group.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"11 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77255287","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}
引用次数: 4
Linear representations of random groups 随机组的线性表示
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-10-02 DOI: 10.1142/S1664360719500164
G. Kozma, A. Lubotzky
{"title":"Linear representations of random groups","authors":"G. Kozma, A. Lubotzky","doi":"10.1142/S1664360719500164","DOIUrl":"https://doi.org/10.1142/S1664360719500164","url":null,"abstract":"We show that for a fixed [Formula: see text], Gromov random groups with any density [Formula: see text] have no nontrivial degree [Formula: see text] representations over any field, a.a.s. This is especially interesting in light of the results of Agol, Ollivier and Wise that when [Formula: see text] such groups have a faithful linear representation over [Formula: see text], a.a.s.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"9 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85667576","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}
引用次数: 4
Minimizer of an isoperimetric ratio on a metric on $${mathbb {R}}^2$$R2 with finite total area 总面积有限的$${mathbb {R}}^2$$ R2度规上等周比的最小化
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-09-25 DOI: 10.1007/s13373-018-0131-3
S. Hsu
{"title":"Minimizer of an isoperimetric ratio on a metric on $${mathbb {R}}^2$$R2 with finite total area","authors":"S. Hsu","doi":"10.1007/s13373-018-0131-3","DOIUrl":"https://doi.org/10.1007/s13373-018-0131-3","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"124 2-3 1","pages":"603-617"},"PeriodicalIF":1.2,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78151519","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}
引用次数: 1
Optimal transport with discrete long-range mean-field interactions 离散远程平均场相互作用的最优输运
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-09-19 DOI: 10.1142/s1664360720500113
Jiakun Liu, G. Loeper
{"title":"Optimal transport with discrete long-range mean-field interactions","authors":"Jiakun Liu, G. Loeper","doi":"10.1142/s1664360720500113","DOIUrl":"https://doi.org/10.1142/s1664360720500113","url":null,"abstract":"We study an optimal transport problem where, at some intermediate time, the mass is either accelerated by an external force field or self-interacting. We obtain the regularity of the velocity potential, intermediate density, and optimal transport map, under the conditions on the interaction potential that are related to the so-called Ma–Trudinger–Wang condition from optimal transport [X.-N. Ma, N. S. Trudinger and X.-J. Wang, Regularity of potential functions of the optimal transportation problems, Arch. Ration. Mech. Anal. 177 (2005) 151–183.].","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"117 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88422863","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}
引用次数: 2
Conjugacy problem in groups with quadratic Dehn function 二次Dehn函数群的共轭问题
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-09-02 DOI: 10.1142/s1664360719500231
A. Olshanskii, M. Sapir
{"title":"Conjugacy problem in groups with quadratic Dehn function","authors":"A. Olshanskii, M. Sapir","doi":"10.1142/s1664360719500231","DOIUrl":"https://doi.org/10.1142/s1664360719500231","url":null,"abstract":"We construct a finitely presented group with quadratic Dehn function and undecidable conjugacy problem. This solves Rips’ problem formulated in 1994.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89665226","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}
引用次数: 7
Embedding of vector-valued Morrey spaces and separable differential operators 向量值Morrey空间的嵌入与可分离微分算子
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-08-20 DOI: 10.1007/S13373-018-0129-X
M. Ragusa, V. Shakhmurov
{"title":"Embedding of vector-valued Morrey spaces and separable differential operators","authors":"M. Ragusa, V. Shakhmurov","doi":"10.1007/S13373-018-0129-X","DOIUrl":"https://doi.org/10.1007/S13373-018-0129-X","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"15 1","pages":"1-23"},"PeriodicalIF":1.2,"publicationDate":"2018-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88442001","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}
引用次数: 4
Matrix biorthogonal polynomials on the real line: Geronimus transformations 实线上的矩阵双正交多项式:格罗尼莫变换
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-08-06 DOI: 10.1007/S13373-018-0128-Y
Gerardo Ariznabarreta, J. C. García-Ardila, Manuel Mañas, F. Marcellán
{"title":"Matrix biorthogonal polynomials on the real line: Geronimus transformations","authors":"Gerardo Ariznabarreta, J. C. García-Ardila, Manuel Mañas, F. Marcellán","doi":"10.1007/S13373-018-0128-Y","DOIUrl":"https://doi.org/10.1007/S13373-018-0128-Y","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"165 7 Suppl 2 1","pages":"1-66"},"PeriodicalIF":1.2,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83327530","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}
引用次数: 19
Weighted Sobolev spaces: Markov-type inequalities and duality 加权Sobolev空间:markov型不等式和对偶性
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-08-01 DOI: 10.1007/S13373-017-0104-Y
F. Marcellán, Yamilet Quintana, José M. Rodríguez
{"title":"Weighted Sobolev spaces: Markov-type inequalities and duality","authors":"F. Marcellán, Yamilet Quintana, José M. Rodríguez","doi":"10.1007/S13373-017-0104-Y","DOIUrl":"https://doi.org/10.1007/S13373-017-0104-Y","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"43 1","pages":"233-256"},"PeriodicalIF":1.2,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86647577","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}
引用次数: 4
Positive solutions for nonlinear parametric singular Dirichlet problems 非线性参数奇异狄利克雷问题的正解
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-07-20 DOI: 10.1142/S1664360719500115
N. Papageorgiou, V. Rǎdulescu, Dušan D. Repovš
{"title":"Positive solutions for nonlinear parametric singular Dirichlet problems","authors":"N. Papageorgiou, V. Rǎdulescu, Dušan D. Repovš","doi":"10.1142/S1664360719500115","DOIUrl":"https://doi.org/10.1142/S1664360719500115","url":null,"abstract":"We consider a nonlinear parametric Dirichlet problem driven by the p-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is ($$p-1$$p-1)-linear near $$+infty $$+∞. The problem is uniformly nonresonant with respect to the principal eigenvalue of $$(-Delta _p,W^{1,p}_0(Omega ))$$(-Δp,W01,p(Ω)). We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter $$lambda >0$$λ>0.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"42 1","pages":"1-22"},"PeriodicalIF":1.2,"publicationDate":"2018-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82427083","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}
引用次数: 41
On the size of Diophantine m-tuples in imaginary quadratic number rings 虚二次数环中丢番图m元组的大小
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-07-05 DOI: 10.1142/S1664360719500206
Nikola Advzaga
{"title":"On the size of Diophantine m-tuples in imaginary quadratic number rings","authors":"Nikola Advzaga","doi":"10.1142/S1664360719500206","DOIUrl":"https://doi.org/10.1142/S1664360719500206","url":null,"abstract":"A Diophantine [Formula: see text]-tuple is a set of [Formula: see text] distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers. We study the same problem in the rings of integers of imaginary quadratic fields. By using a gap principle proven by Diophantine approximations, we show that [Formula: see text]. Our proof is relatively simple compared to the proofs of similar results in positive integers.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"29 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86214081","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}
引用次数: 10
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