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

作者：Almeida Alexandre; Caetano Antonio

来源：Journal of Functional Analysis, 2016, 270(5): 1888-1921.

DOI：10.1016/j.jfa.2015.11.010

• Variable exponents
• Besov-Triebel-Lizorkin spaces
• Atoms and Molecules
• Sobolev embeddings

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.

• 出版日期2016-3-1