Shear Anisotropic Inhomogeneous Besov And Triebel-Lizorkin Spaces In $R^d$

TL;DR

This paper introduces shear anisotropic inhomogeneous Besov and Triebel-Lizorkin spaces, providing their characterizations, embeddings, and a reproducing identity, thereby advancing the mathematical framework for shearlet-based distribution analysis.

Contribution

It defines new shear anisotropic inhomogeneous function spaces, establishes their properties, and explores their relationships with classical isotropic spaces.

Findings

Characterization of shear anisotropic spaces

Reproducing identity in distribution class

Sobolev-type and classical embeddings

Abstract

We define distribution spaces of a sequence of convolutions of a set of distributions with smooth functions, the shearlet system. Then, we define associated sequence spaces and prove characterizations. We also show a reproducing identity in the class of distributions. Finally, we prove Sobolev-type embeddings within the shear anisotropic inhomogeneous spaces and embeddings between (classical dyadic) isotropic inhomogeneous spaces and shear anisotropic inhomogeneous spaces.