Resolution of open problems via Orlicz-Zygmund spaces and new geometric properties of Morrey spaces in the Besov sense with non-standard growth

초록

In this paper, we introduced a novel norm structure and corresponding modular for Orlicz-Zygmund spaces, designed to capture summability and integrability properties under non-standard growth conditions. Moreover, we established the Hermite-Hadamard inequalities and gave a positive answer to the open problem 3.11 of Almeida and H & auml;st & ouml; in their article (Besov spaces with variable smoothness and integrability, J. Funct. Anal., 258 (2010), 1628-1655), since the Hermite-Hadamard inequalities improve triangular-type inequalities. In addition, we explored some new structural properties of Besov-type Morrey spaces of summability and integrability. Furthermore, we addressed an open problem concerning the compactness of Morrey-type spaces characterized by summability and integrability properties. This problem was originally posed by Peter H & auml;st & ouml; during the conference "Nonstandard Growth Phenomena", held in Turku, Finland, from August 29 to 31, 2017.

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