Greedy bases in variable Lebesgue spaces

TL;DR

This paper analyzes wavelet bases in variable Lebesgue spaces, computing democracy functions and establishing Lebesgue type inequalities, with extensions to weighted spaces and Triebel-Lizorkin spaces.

Contribution

It introduces methods to compute democracy functions for wavelet bases in variable Lebesgue spaces and extends results to related weighted and Triebel-Lizorkin spaces.

Findings

Computed democracy functions for wavelet bases in variable Lebesgue spaces

Established Lebesgue type inequalities for these bases

Extended techniques to weighted and Triebel-Lizorkin spaces

Abstract

We compute the right and left democracy functions of admissible wavelet bases in variable Lebesgue spaces defined on $R^n$. As an application we give Lebesgue type inequalities for these wavelet bases. We also show that our techniques can be easily modified to prove analogous results for weighted variable Lebesgue spaces and variable exponent Triebel-Lizorkin spaces.