Besov class via heat semigroup on Dirichlet spaces I: Sobolev type\n inequalities

2018/11/10 by Patricia Alonso Ruiz, Alonso-Ruiz, Patricia, Fabrice Baudoin +10 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1811.04267

openalex publication_date 2018/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce heat semigroup-based Besov classes in the general framework of\nDirichlet spaces. General properties of those classes are studied and\nquantitative regularization estimates for the heat semigroup in this scale of\nspaces are obtained. As a highlight of the paper, we obtain a far reaching\nL^p-analogue, p \≥ 1, of the Sobolev inequality that was proved for p=2\nby N. Varopoulos under the assumption of ultracontractivity for the heat\nsemigroup. The case p=1 is of special interest since it yields isoperimetric\ntype inequalities.\n

Cited by

• Fractional Heat Semigroup Characterization of Distances from Functions in Lipschitz Spaces to Their Subspaces

Related

• Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates
• Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates
• BV functions and fractional Laplacians on Dirichlet spaces
• The semigroup generated by the Dirichlet Laplacian of fractional order
• Bilinear estimates in Besov spaces generated by the Dirichlet Laplacian