Lipschitz Invariance of Critical Exponents on Besov Spaces

• 作者: Qingsong Gu Hui Rao
• 来源期刊: 分析、理论与应用（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 457-467
• 页数: 11页
• 语种: 英文
• DOI: 10.4208/ata.OA-SU5

摘要

In this paper we prove that the critical exponents of Besov spaces on a com-pact set possessing an Ahlfors regular measure is an invariant under Lipschitz trans-forms.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.