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2016 Fréchet Envelopes of Nonlocally Convex Variable Exponent Hörmander Spaces
Joaquín Motos, María Jesús Planells, César F. Talavera
Abstr. Appl. Anal. 2016: 1-9 (2016). DOI: 10.1155/2016/1393496


We show that the dual Bp·locΩ of the variable exponent Hörmander space Bp(·)loc(Ω) is isomorphic to the Hörmander space Bc(Ω) (when the exponent p(·) satisfies the conditions 0<p-p+1, the Hardy-Littlewood maximal operator M is bounded on Lp(·)/p0 for some 0<p0<p- and Ω is an open set in Rn) and that the Fréchet envelope of Bp(·)loc(Ω) is the space B1loc(Ω). Our proofs rely heavily on the properties of the Banach envelopes of the p0-Banach local spaces of Bp(·)loc(Ω) and on the inequalities established in the extrapolation theorems in variable Lebesgue spaces of entire analytic functions obtained in a previous article. Other results for p(·)p, 0<p<1, are also given (e.g., all quasi-Banach subspace of Bploc(Ω) is isomorphic to a subspace of lp, or l is not isomorphic to a complemented subspace of the Shapiro space hp-). Finally, some questions are proposed.


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Joaquín Motos. María Jesús Planells. César F. Talavera. "Fréchet Envelopes of Nonlocally Convex Variable Exponent Hörmander Spaces." Abstr. Appl. Anal. 2016 1 - 9, 2016.


Received: 30 May 2016; Accepted: 27 September 2016; Published: 2016
First available in Project Euclid: 17 December 2016

zbMATH: 54.0036.03
MathSciNet: MR3574250
Digital Object Identifier: 10.1155/2016/1393496

Rights: Copyright © 2016 Hindawi

Vol.2016 • 2016
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