TY - JOUR
T1 - Lipschitz Invariance of Critical Exponents on Besov Spaces
AU - Gu , Qingsong
AU - Rao , Hui
JO - Analysis in Theory and Applications
VL - 4
SP - 457
EP - 467
PY - 2020
DA - 2020/12
SN - 36
DO - http://doi.org/10.4208/ata.OA-SU5
UR - https://global-sci.org/intro/article_detail/ata/18463.html
KW - Lipschitz invariant, Besov space, critical exponents, walk dimension, heat kernel.
AB - <p style="text-align: justify;">In this paper we prove that the critical exponents of Besov spaces on a compact set possessing an Ahlfors regular measure is an invariant under Lipschitz transforms. Under mild conditions, the critical exponent of Besov spaces of certain self-similar sets coincides with the walk dimension, which plays an important role in the analysis on fractals. As an application, we show examples having different critical exponents are not Lipschitz equivalent.</p>