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Asian Journal of Mathematics
Volume 27 (2023)
Number 4
BV functions and fractional Laplacians on Dirichlet spaces
Pages: 441 – 466
DOI: https://dx.doi.org/10.4310/AJM.2023.v27.n4.a1
Authors
Abstract
We study bounded variation (BV) and fractional Sobolev functional spaces, $L^p$ Besov critical exponents and isoperimetric and Sobolev inequalities associated with fractional Laplacians on metric measure spaces. The main tool is the theory of heat semigroup based Besov classes in Dirichlet Metric Measure Spaces that was introduced by the authors in previous works.
Keywords
Besov critical exponents, isoperimetric and Sobolev inequalities, fractional Laplacians, metric measure spaces, heat semigroup, Dirichlet spaces
2010 Mathematics Subject Classification
26A45, 28A80, 31C25, 46E35, 60J45
The authors dedicate this paper to the memory of Ka-Sing Lau, whose important contributionsto the general theory of Markov processes and Dirichlet forms on fractals and metricmeasure spaces, especially in the papers [43, 44, 48, 49], influenced the development of thiswork.
Received 31 December 2022
Accepted 25 July 2023
Published 10 July 2024