Duality of Variable Exponent Triebel-Lizorkin and Besov SpacesReport as inadecuate




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Journal of Function Spaces and ApplicationsVolume 2012 2012, Article ID 361807, 19 pages

Research ArticleDepartment of Mathematics, Graduate School of Science and Engineering, Chuo University, 13-27 Kasuga 1-chome, Bunkyoku, Tokyo 192-0393, Japan

Received 12 December 2010; Accepted 25 May 2011

Academic Editor: V. M. Kokilashvili

Copyright © 2012 Takahiro Noi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We will prove the duality and reflexivity of variable exponent Triebel-Lizorkin and Besov spaces. It was shown by many authors that variable exponent Triebel-Lizorkin spaces coincide with variable exponent Besselpotential spaces, Sobolev spaces, and Lebesgue spaces when appropriate indices are chosen. In consequence of the results, these variable exponent function spaces are shown to be reflexive.





Author: Takahiro Noi

Source: https://www.hindawi.com/



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