Anisotropic, Mixed-Norm Lizorkin--Triebel Spaces and Diffeomorphic Maps

TL;DR

This paper studies how anisotropic Lizorkin--Triebel spaces with mixed norms behave under coordinate changes, providing general invariance results across various Euclidean domains.

Contribution

It establishes the invariance properties of anisotropic mixed-norm Lizorkin--Triebel spaces under diffeomorphic coordinate transformations.

Findings

Invariance of these spaces under coordinate transformations.

Applicability to Euclidean spaces, open sets, and cylindrical domains.

General theoretical framework for anisotropic mixed-norm function spaces.

Abstract

This article gives general results on invariance of anisotropic Lizorkin--Triebel spaces with mixed norms under coordinate transformations on Euclidean space, open sets and cylindrical domains.