Density, Duality and Preduality in Grand Variable Exponent Lebesgue and Morrey Spaces

2017/10/06 by Alexander Meskhi, Yoshihiro Sawano, Meskhi, Alexander +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #math.FA

paper · pdf · doi:10.48550/arxiv.1710.02383

15 pages

arxiv created 2017/10/06 · openalex publication_date 2017/10/06 · arxiv updated 2017/10/09 · openalex created_date 2017/10/20 · openalex updated_date 2026/07/28

Abstract

In this note some structural properties of grand variable exponent Lebesgue/ Morrey spaces over spaces of homogeneous type are obtained. In particular, it is proved that the closure of the class of bounded functions and the closure of classical Morrey space in grand variable exponent Morrey space coincide if the measure of the underlying space is finite. Moreover, we get two different characterizations of this class. Further, duality and preduality of grand variable exponent Lebesghue space defined on quasi-metric measure spaces with sigma-finite measure are obtained, which is new even when underlying measure is finite.

Citations

• On the solutions of quasi-linear elliptic partial differential equations

Related

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• Integral Operators in Grand Morrey Spaces
• A thought on generalized Morrey spaces
• Riesz type potential operators in generalized grand Morrey spaces
• Ergodic Theorem in Grand Variable Exponent Lebesgue Spaces