Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications

Abstract

In this article we study atomic and molecular decompositions in $2$-microlocal Besov and Triebel--Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves. As an application, we give a simple proof for the denseness of the Schwartz class in such spaces. Some other properties, like Sobolev embeddings, are also obtained via atomic representations.

27 pages

References in corpus (1)

• On 2-microlocal spaces with all exponents variable

Cited by in corpus (6)

• Variable Weak Hardy Spaces and Their Applications
• On 2-microlocal spaces with all exponents variable
• Variable exponent Besov-Morrey spaces
• Density results for Sobolev, Besov and Triebel--Lizorkin spaces on rough sets
• Variable Martingale Hardy Spaces and Their Applications in Fourier Analysis
• Decompositions with atoms and molecules for variable exponent Triebel-Lizorkin-Morrey spaces