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Interpolation of compact bilinear operators 紧双线性算子的插值
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2019-04-13 DOI: 10.1142/s1664360720500022
M. Mastyło, E. B. Silva
{"title":"Interpolation of compact bilinear operators","authors":"M. Mastyło, E. B. Silva","doi":"10.1142/s1664360720500022","DOIUrl":"https://doi.org/10.1142/s1664360720500022","url":null,"abstract":"This paper is devoted to the study of the stability of the compactness property of bilinear operators acting on the products of interpolated Banach spaces. We prove one-sided compactness results for bilinear operators on products of Banach spaces generated by abstract methods of interpolation, in the sense of Aronszajn and Gagliardo. To get these results, we prove a key one-sided bilinear interpolation theorem on compactness for bilinear operators on couples satisfying an extra approximation property. We give applications to general cases, including Peetre’s method and the general real interpolation methods.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81568212","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: 5
Lq-Estimates for stationary Stokes system with coefficients measurable in one direction 系数在一个方向上可测的平稳Stokes系统的lq估计
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2019-04-01 DOI: 10.1142/s1664360719500048
Hongjie Dong, Doyoon Kim
{"title":"Lq-Estimates for stationary Stokes system with coefficients measurable in one direction","authors":"Hongjie Dong, Doyoon Kim","doi":"10.1142/s1664360719500048","DOIUrl":"https://doi.org/10.1142/s1664360719500048","url":null,"abstract":"We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori [Formula: see text]-estimates for any [Formula: see text] when the coefficients are merely measurable functions in one fixed direction. For the system on bounded Lipschitz domains with a small Lipschitz constant, we obtain a [Formula: see text]-estimate and prove the solvability for any [Formula: see text] when the coefficients are merely measurable functions in one direction and have locally small mean oscillations in the orthogonal directions in each small ball, where the direction is allowed to depend on the ball.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79515697","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: 15
Smoothness of functions versus smoothness of approximation processes 函数的平滑性和近似过程的平滑性
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2019-03-01 DOI: 10.1142/s1664360720300029
Yurii Kolomoitsev, S. Tikhonov
{"title":"Smoothness of functions versus smoothness of approximation processes","authors":"Yurii Kolomoitsev, S. Tikhonov","doi":"10.1142/s1664360720300029","DOIUrl":"https://doi.org/10.1142/s1664360720300029","url":null,"abstract":"We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed: The first based on geometric properties of Banach spaces and the second on Littlewood–Paley and Hörmander-type multiplier theorems. In particular, we obtain new sharp inequalities for measures of smoothness given by the [Formula: see text]-functionals or moduli of smoothness. As examples of approximation processes we consider best polynomial and spline approximations, Fourier multiplier operators on [Formula: see text], [Formula: see text], [Formula: see text], nonlinear wavelet approximation, etc.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79567788","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: 9
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
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