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Title: Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications
Author: Almeida, Alexandre
Caetano, António
Keywords: Variable exponents
Besov–Triebel–Lizorkin spaces
Atoms and molecules
Sobolev embeddings
Issue Date: 28-Nov-2015
Publisher: Elsevier
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.
Peer review: yes
DOI: 10.1016/j.jfa.2015.11.010
ISSN: 0022-1236
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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