Sobolev's theorem and duality for Herz-Morrey spaces of variable exponent | Zendy

Yoshihiro Mizuta | Zendy; Takao Ohno | Zendy

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Sobolev's theorem and duality for Herz-Morrey spaces of variable exponent

Author(s) -

Yoshihiro Mizuta,

Takao Ohno

Publication year - 2014

Publication title -

annales academiae scientiarum fennicae mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.865

H-Index - 37

eISSN - 1798-2383

pISSN - 1239-629X

DOI - 10.5186/aasfm.2014.3913

Subject(s) - duality (order theory) , sobolev space , mathematics , pure mathematics , variable (mathematics) , mathematical analysis

In this paper, we consider the Herz-Morrey space H p(·),q,! {x0} (G) of variable exponent consisting of all measurable functions f on a bounded open set G ⊂ R n satisfying kfk H p(·),q,! {x0} (G) = ˆ 2dG H p(·),q,! (G),H p(·),q,! {x0} (G) and ˜ H p(·),q,! (G). Following Fiorenza-Rakotoson (18), Di Fratta-Fiorenza (17) and Gogatishvili-Mustafayev (19), we next discuss the duality properties among these Herz- Morrey spaces.

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