The Besov capacity in metric spaces

被引：10

作者：

Nuutinen, Juho ^{[1
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, POB 35, FI-40014 Jyvaskyla, Finland

来源：

ANNALES POLONICI MATHEMATICI | 2016年 / 117卷 / 01期

基金：

芬兰科学院;

关键词：

Besov spaces; capacity; metric spaces; TRIEBEL-LIZORKIN SPACES; SOBOLEV SPACES; EXTENSION;

D O I：

10.4064/ap3843-4-2016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a capacity theory based on a definition of Hajlasz Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are gamma-medians, for which we also prove a new version of a Poincare type inequality.

引用

页码：59 / 78

页数：20

共 50 条

[31] Lifting in Besov spaces [J].

Mironescu, Petru ;

Russ, Emmanuel ;

Sire, Yannick .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 193

[32] Heat-Semigroup-Based Besov Capacity on Dirichlet Spaces and Its Applications [J].

Xie, Xiangyun ;

Wang, Haihui ;

Liu, Yu .

MATHEMATICS, 2024, 12 (07)

[33] Besov Spaces for the Schrodinger Operator with Barrier Potential [J].

Benedetto, John J. ;

Zheng, Shijun .

COMPLEX ANALYSIS AND OPERATOR THEORY, 2010, 4 (04) :777-811

[34] EXTENSION AND RESTRICTION THEOREMS IN ANISOTROPIC BESOV SPACES [J].

Chang, Tongkeun .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2010, 12 (02) :265-294

[35] Pseudodifferential Operators on Besov Spaces of Variable Smoothness [J].

Kryakvin, V. D. ;

Rabinovich, V. S. .

MATHEMATICAL NOTES, 2018, 104 (3-4) :545-558

[36] A Plancherel-Polya Inequality in Besov Spaces on Spaces of Homogeneous Type [J].

Jaming, Philippe ;

Negreira, Felipe .

JOURNAL OF GEOMETRIC ANALYSIS, 2019, 29 (02) :1571-1582

[37] Triebel-Lizorkin Spaces on Metric Spaces via Hyperbolic Fillings [J].

Bonk, Mario ;

Saksman, Eero ;

Soto, Tomas .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2018, 67 (04) :1625-1663

[38] Besov and Holder spaces on spaces of homogeneous type [J].

Han, Yongshen ;

Lee, Ming-Yi ;

Lin, Chin-Cheng .

STUDIA MATHEMATICA, 2020, 255 (03) :219-263

[39] Shape optimization problems on metric measure spaces [J].

Buttazzo, Giuseppe ;

Velichkov, Bozhidar .

JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 264 (01) :1-33

[40] Nuclear Embeddings of Besov Spaces into Zygmund Spaces [J].

Cobos, Fernando ;

Edmunds, David E. ;

Kuehn, Thomas .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2020, 26 (01)

← 1 2 3 4 5 →