Year: 2025
Author: Pierre-A. Vuillermot
Communications in Mathematical Analysis and Applications, Vol. 4 (2025), Iss. 2 : pp. 285–295
Abstract
In this article we introduce a new class of weighted sequence spaces of Sobolev type and prove several compact embedding theorems for them. It is our contention that the chosen class is general enough so as to allow applications in various areas of mathematics and mathematical physics. In particular, our results constitute a generalization of those compact embeddings recently obtained in relation to the spectral analysis of a class of master equations arising in non-equilibrium statistical mechanics. As a byproduct of our considerations, we also prove a theorem of Pitt’s type asserting that under some conditions every linear bounded operator acting between such weighted spaces is compact.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmaa.2025-0005
Communications in Mathematical Analysis and Applications, Vol. 4 (2025), Iss. 2 : pp. 285–295
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Sobolev sequence spaces Pitt’s property.