Korevaar-Schoen-Sobolev spaces and critical exponents in metric measure spaces

被引：1
作者：
Baudoin, Fabrice [1 ]
机构：
[1] Aarhus Univ, Dept Math, Ny Munkegade 118, DK-8000 Aarhus, Denmark
来源：
ANNALES FENNICI MATHEMATICI | 2024年 / 49卷 / 02期
关键词：
Fractals; Sobolev spaces; Korevaar-Schoen space; HEAT KERNELS; POINCARE INEQUALITIES; DIFFUSION-PROCESSES; DIRICHLET FORMS; BROWNIAN-MOTION; P-ENERGY; FRACTALS; PROOF; SETS;
D O I：
10.54330/afm.147513
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We survey, unify and present new developments in the theory of Korevaar-Schoen- Sobolev spaces on metric measure spaces. While this theory coincides with those of Cheeger and Shanmugalingam if the space is doubling and supports a Poincar & eacute; inequality, it offers new perspectives in the context of fractals for which the approach by weak upper gradients is inadequate.
引用
收藏
页码：487 / 527
页数：41
相关论文
共 66 条
  • [1] Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates
    Alonso-Ruiz, Patricia
    Baudoin, Fabrice
    Chen, Li
    Rogers, Luke
    Shanmugalingam, Nageswari
    Teplyaev, Alexander
    [J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (05)
  • [2] Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates
    Alonso-Ruiz, Patricia
    Baudoin, Fabrice
    Chen, Li
    Rogers, Luke
    Shanmugalingam, Nageswari
    Teplyaev, Alexander
    [J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2020, 59 (03)
  • [3] A simple proof of reflexivity and separability of N1,P Sobolev spaces
    Alvarado, Ryan
    Hajlasz, Piotr
    Maly, Lukas
    [J]. ANNALES FENNICI MATHEMATICI, 2023, 48 (01): : 255 - 275
  • [4] Bakry D, 1995, INDIANA U MATH J, V44, P1033
  • [5] A new fractal dimension: The topological Hausdorff dimension
    Balka, Richard
    Buczolich, Zoltan
    Elekes, Marton
    [J]. ADVANCES IN MATHEMATICS, 2015, 274 : 881 - 927
  • [6] Barlow M.T., 1998, LECT NOTES MATH, P1
  • [7] Stability of parabolic Harnack inequalities on metric measure spaces
    Barlow, Martin T.
    Bass, Richard F.
    Kumagai, Takashi
    [J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2006, 58 (02) : 485 - 519
  • [8] Sobolev spaces and Poincare inequalities on the Vicsek fractal
    Baudoin, Fabrice
    Chen, Li
    [J]. ANNALES FENNICI MATHEMATICI, 2023, 48 (01): : 3 - 26
  • [9] ON KIGAMI'S CONJECTURE OF THE EMBEDDING Wp(K) ⊂ C(K)
    Cao, Shiping
    Chen, Zhen-Qing
    Kumagai, Takashi
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (08) : 3393 - 3402
  • [10] p-energies on p.c.f. self-similar sets
    Cao, Shiping
    Gu, Qingsong
    Qiu, Hua
    [J]. ADVANCES IN MATHEMATICS, 2022, 405
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