Characterisation by Local Means of Anisotropic Lizorkin--Triebel Spaces with Mixed Norms

Abstract

This is a contribution to the theory of Lizorkin--Triebel spaces having mixed Lebesgue norms and quasi-homogeneous smoothness. We discuss their characterisation in terms of general quasi-norms based on convolutions. In particular, this covers the case of local means, in Triebel's terminology. The main step is an extension of some crucial inequalities due to Rychkov to the case with mixed norms.

19 pages. Final version. Appeared in Journal for analysis and its applications. (Two references are updated.)

References in corpus (3)

• On the trace problem for Triebel--Lizorkin spaces with mixed norms
• Anisotropic, Mixed-Norm Lizorkin--Triebel Spaces and Diffeomorphic Maps
• Pointwise estimates of pseudo-differential operators

Cited by in corpus (5)

• Wavelet transforms for homogeneous mixed-norm Triebel--Lizorkin spaces
• Anisotropic Lizorkin--Triebel Spaces with Mixed Norms --- Traces on Smooth Boundaries
• Anisotropic, Mixed-Norm Lizorkin--Triebel Spaces and Diffeomorphic Maps
• New Estimates of Rychkov's Universal Extension Operator for Lipschitz Domains and Some Applications
• Atomic and Littlewood-Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications