An analogue of the Littlewood-Paley theorem for orthoprojectors onto wavelet subspaces

TL;DR

This paper establishes a Littlewood-Paley type theorem for wavelet subspace orthoprojectors derived from nonisotropic multiresolution analysis, extending classical harmonic analysis results to wavelet frameworks.

Contribution

It introduces an analogue of the Littlewood-Paley theorem specifically for orthoprojectors onto wavelet subspaces in a nonisotropic multiresolution setting.

Findings

Proves a Littlewood-Paley type inequality for wavelet subspace orthoprojectors.

Extends classical harmonic analysis results to nonisotropic wavelet frameworks.

Provides theoretical foundation for wavelet analysis in nonisotropic contexts.

Abstract

The article proves an assertion analogous to the Littlewood-Paley theorem for the orthoprojectors onto wavelet subspaces corresponding to the nonisotropic multiresolution analysis generated as tensor product of smooth scaling single-variable functions sufficiently rapidly vanishing at infinity.