Heat-Semigroup-Based Besov Capacity on Dirichlet Spaces and Its Applications

Xiangyun Xie (), Haihui Wang and Yu Liu
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Xiangyun Xie: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
Haihui Wang: School of Mathematical Sciences, Beihang University, Beijing 100191, China
Yu Liu: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Mathematics, 2024, vol. 12, issue 7, 1-17

Abstract: In this paper, we investigate the Besov space and the Besov capacity and obtain several important capacitary inequalities in a strictly local Dirichlet space, which satisfies the doubling condition and the weak Bakry–Émery condition. It is worth noting that the capacitary inequalities in this paper are proved if the Dirichlet space supports the weak ( 1 , 2 ) -Poincaré inequality, which is weaker than the weak ( 1 , 1 ) -Poincaré inequality investigated in the previous references. Moreover, we first consider the strong subadditivity and its equality condition for the Besov capacity in metric space.

Keywords: Besov space; Dirichlet space; heat kernel; capacity; Sobolev inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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