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In this study, we establish some new characterizations for a class of anisotropic Herz spaces in which all exponents are considered as variables. We also provide a description of these spaces based on bloc decomposition. As an application, we investigate the boundedness of certain sublinear operators within these function spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove that Marcinkiewicz integral operators are bounded from Kpα(⋅),q(⋅)(Rn) to Kpα(⋅),q(⋅)(Rn) when the parameters α(⋅); p(⋅) and q(⋅) satisfies some conditions. Also, we prove the boundedness of Ā on variable Herz-type Hardy spaces H Kα(⋅);q(⋅) p(⋅) (Rn). [ABSTRACT FROM AUTHOR]