A characterisation of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels

2015/02/24 by Huy‐Qui Bui, Bui, Huy-Qui, Timothy Candy +1 · 1 citation
Mathematics · #42B25 #46E35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1502.06836

openalex publication_date 2015/02/24 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We give a complete characterisation of the spaces B^α_p,q and F^α_p,q by using a non-smooth kernel satisfying near minimal conditions. The tools used include a Stromberg-Torchinsky type estimate for certain maximal functions and the concept of a distribution of finite growth, inspired by Stein. Moreover, our exposition also makes essential use of a number of refinements of the well-known Calderon reproducing formula. The results are then applied to obtain the characterisation of these spaces via a fractional derivative of the Poisson kernel.

Cited by

• Asymptotic Behaviour of fractional seminorms

Related

• Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces
• Function spaces of logarithmic smoothness: embeddings and characterizations
• Pointwise and grand maximal function characterizations of Besov-type and Triebel-Lizorkin-type spaces
• Function Spaces via Fractional Poisson Kernel on Carnot Groups and Applications
• Characterizations of Besov and Triebel-Lizorkin Spaces via Averages on Balls