Inhomogeneous shearlet coorbit spaces

TL;DR

This paper develops inhomogeneous shearlet coorbit spaces linked to the continuous shearlet transform and weighted Lebesgue spaces, introducing a new shearlet frame and analyzing its properties to establish Banach space structure.

Contribution

It introduces inhomogeneous shearlet coorbit spaces, constructs a new shearlet frame, and generalizes existing methods to prove these spaces are Banach spaces.

Findings

Established inhomogeneous shearlet coorbit spaces related to weighted Lebesgue spaces.

Constructed an inhomogeneous shearlet frame for $L_2(\

Abstract

In this paper we establish inhomogeneous coorbit spaces related to the continuous shearlet transform and the weighted Lebesgue spaces $L_{p,v}, p\geq 1,$ for certain weights $v$. We present an inhomogeneous shearlet frame for $L_2(\mathbb{R}^d)$ which gives rise to a reproducing kernel $R_\mathfrak{F}$ that is not contained in the space $\mathcal{A}_{1,m_v}$. To show that the inhomogeneous shearlet coorbit spaces are Banach spaces we introduce a generalization of the approach of Fornasier, Rauhut and Ullrich.