Interpolatory Estimates, Riesz Transforms and Wavelet Projections

TL;DR

This paper establishes a mathematical relationship between directional wavelet projections and Riesz transforms using interpolatory estimates, advancing understanding of wavelet systems and their properties.

Contribution

It introduces new interpolatory estimates linking wavelet projections and Riesz transforms based on H"older regularity, extending prior work on Haar projections.

Findings

Directional wavelet projections and Riesz transforms are related by interpolatory estimates.

The exponents of interpolation depend on the H"older estimates of the wavelet system.

The work extends previous results on Haar projections to more general wavelet systems.

Abstract

We prove that directional wavelet projections and Riesz transforms are related by interpolatory estimates. The exponents of interpolation depend on the H\"older estimates of the wavelet system. This paper complements and continues previous work on Haar projections.