Anisotropic Herz-type Hardy spaces with variable exponent and their applications
More and more classical spaces are generalized to the setting with variable exponent. In the paper under review, a class of anisotropic Herz-type Hardy spaces with variable exponent associated with a non-isotropic dilation on \(\mathbb R^n\) is introduced, and characterizations of these spaces are established in terms of atomic and molecular decompositions. As a preceding source for anisotropic Hardy type spaces in a ``usual'' metric, Bownik's work is righteously referred to. It is also worth adding \textit{S. Dekel} and \textit{T. Weissblat} [Math. Nachr. 285, No. 17--18, 2078--2092 (2012; Zbl 1261.42032)] The obtained results are applied to show that these Herz-type Hardy spaces are a proper substitute for earlier studied Herz-type spaces with variable exponent. Further, interpolation of operators on the anisotropic Herz-type Hardy spaces with variable exponent is discussed.
scientific article; zbMATH DE number 7011032