Wiener-Lebesgue Point Property for Sobolev Functions on Metric Spaces

被引：0
作者：
Bhat, M. Ashraf [1 ]
Kosuru, G. Sankara Raju [1 ]
机构：
[1] Indian Inst Technol Ropar, Dept Math, Rupnagar 140001, Punjab, India
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2024年 / 21卷 / 08期
关键词：
Lebesgue points; Sobolev spaces; doubling measures; capacity; CONTINUITY;
D O I：
10.1007/s00009-024-02764-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish a Wiener-type integral condition for first-order Sobolev functions defined on a complete, doubling metric measure space supporting a Poincar & eacute; inequality. It is stronger than the Lebesgue point property, except for a marginal increase in the capacity of the set of non-Lebesgue points.
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页数：13
相关论文
共 14 条
  • [1] Bjorn A, 2011, EMS TRACTS MATH, V17, P1, DOI 10.4171/099
  • [2] The Weak Cartan Property for the p-fine Topology on Metric Spaces
    Bjorn, Anders
    Bjorn, Jana
    Latvala, Visa
    [J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2015, 64 (03) : 915 - 941
  • [3] Fine continuity on metric spaces
    Bjorn, Jana
    [J]. MANUSCRIPTA MATHEMATICA, 2008, 125 (03) : 369 - 381
  • [4] Hajlasz P, 1996, POTENTIAL ANAL, V5, P403
  • [5] Hajlasz P, 1998, REV MAT IBEROAM, V14, P601
  • [6] Hajlasz P., 2002, Sobolev Spaces on Metric-measure Spaces. Heat kernels and analysis on manifolds, graphs, and metric spaces, P173
  • [7] Quasiconformal maps in metric spaces with controlled geometry
    Heinonen, J
    Koskela, P
    [J]. ACTA MATHEMATICA, 1998, 181 (01) : 1 - 61
  • [8] Heinonen Juha, 2015, NEW MATH MONOGRAPHS, V27, DOI 10.1017/CBO9781316135914
  • [9] THE WIENER TEST AND POTENTIAL ESTIMATES FOR QUASI-LINEAR ELLIPTIC-EQUATIONS
    KILPELAINEN, T
    MALY, J
    [J]. ACTA MATHEMATICA, 1994, 172 (01) : 137 - 161
  • [10] Kinnunen J, 2002, REV MAT IBEROAM, V18, P685
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