Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates

abstract

• We introduce the class of bounded variation (BV) functions in a general framework of strictly local Dirichlet spaces with doubling measure. Under the 2-Poincar'e inequality and a weak Bakry-'Emery curvature type condition, this BV class is identified with the heat semigroup based Besov class $mathbf{B}^{1,1/2}(X)$ that was introduced in our previous paper. Assuming furthermore a quasi Bakry-'Emery curvature type condition, we identify the Sobolev class $W^{1,p}(X)$ with $mathbf{B}^{p,1/2}(X)$ for $p>1$. Consequences of those identifications in terms of isoperimetric and Sobolev inequalities with sharp exponents are given.

published proceedings

• CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

author list (cited authors)

• Alonso-Ruiz, P., Baudoin, F., Chen, L. i., Rogers, L., Shanmugalingam, N., & Teplyaev, A.

citation count

• 5

complete list of authors

• Alonso-Ruiz, Patricia||Baudoin, Fabrice||Chen, Li||Rogers, Luke||Shanmugalingam, Nageswari||Teplyaev, Alexander

publisher

• Springer Nature  Publisher

published in

• Calculus of Variations and Partial Differential Equations  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4902 Mathematical Physics
• 4904 Pure Mathematics
• 4905 Statistics
• Math.ap
• Math.fa
• Math.pr

Digital Object Identifier (DOI)

• 10.1007/s00526-020-01750-4

start page

• 103

volume

• 59

issue

• 3

URL

• http://dx.doi.org/10.1007/s00526-020-01750-4