TY - JOUR
T1 - Besov class via heat semigroup on Dirichlet spaces II
T2 - BV functions and Gaussian heat kernel estimates
AU - Alonso-Ruiz, Patricia
AU - Baudoin, Fabrice
AU - Chen, Li
AU - Rogers, Luke
AU - Shanmugalingam, Nageswari
AU - Teplyaev, Alexander
N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - We introduce the class of bounded variation (BV) functions in a general framework of strictly local Dirichlet spaces with doubling measure. Under the 2-Poincaré inequality and a weak Bakry–Émery curvature type condition, this BV class is identified with the heat semigroup based Besov class B1 , 1 / 2(X) that was introduced in our previous paper. Assuming furthermore a quasi Bakry–Émery curvature type condition, we identify the Sobolev class W1 , p(X) with Bp , 1 / 2(X) for p> 1. Consequences of those identifications in terms of isoperimetric and Sobolev inequalities with sharp exponents are given.
AB - We introduce the class of bounded variation (BV) functions in a general framework of strictly local Dirichlet spaces with doubling measure. Under the 2-Poincaré inequality and a weak Bakry–Émery curvature type condition, this BV class is identified with the heat semigroup based Besov class B1 , 1 / 2(X) that was introduced in our previous paper. Assuming furthermore a quasi Bakry–Émery curvature type condition, we identify the Sobolev class W1 , p(X) with Bp , 1 / 2(X) for p> 1. Consequences of those identifications in terms of isoperimetric and Sobolev inequalities with sharp exponents are given.
UR - http://www.scopus.com/inward/record.url?scp=85085192407&partnerID=8YFLogxK
U2 - 10.1007/s00526-020-01750-4
DO - 10.1007/s00526-020-01750-4
M3 - Journal article
AN - SCOPUS:85085192407
SN - 0944-2669
VL - 59
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 3
M1 - 103
ER -