New 2-microlocal Besov and Triebel-Lizorkin spaces via the Littlewood-Paley decomposition

TL;DR

This paper introduces new 2-microlocal Besov and Triebel-Lizorkin spaces using Littlewood-Paley decomposition, providing characterizations and boundedness results for operators, with applications in oscillations and differences.

Contribution

It develops novel 2-microlocal function spaces with multiple characterizations and operator boundedness results, expanding the analytical framework for these spaces.

Findings

Characterizations via $$-transform, atomic, molecular, and wavelet decompositions

Boundedness of Calderf3n-Zygmund and pseudo-differential operators

Characterizations through oscillations and differences

Abstract

In this paper we introduce and investigate new 2-microlocal Besov and Triebel-Lizorkin space via the Littlewood-Paly decomposition. We establish characterizations of these function spaces by the $phi$-transform, the atomic and molecular decomposition and the wavelet decomposition. As applications we prove boundedness of Caldeon-Zygmund operators and the pseudo-differential operators on the function spaces. Moreover, we give characterizations via oscillations and differences.