Some Aspects of B-Harmonic Analysis

Abstract

In this work we introduce and investigate the function spaces, integral operators, generated by the Bessel differential operators, Bessel shift operators and Bessel transformations. We investigate also the boundedness of anisotropic B-maximal functions M B and the anisotropic B-Riesz potentials R α B on the anisotropic B-Morrey spaces L γ p,λ,α , B- BMO spaces BMO γ,α . Note that, the isotropic Hardy-Littlewood-Bessel maximal functions (B-maximal functions), Morrey-Bessel (B-Morrey) and BMO-Bessel (B-BMO) spaces were introduced and studied in [1]. We study also the anisotropic Riesz-Bessel potential (B-potential) in the anisotropic Morrey-Bessel and the anisotropic BMO-Bessel spaces. We obtain a theorem analogous to the Sobolev theorem, for the anisotropic Riesz-Bessel potential in anisotropic Morrey-Bessel spaces (see [2]).KeywordsIntegral OperatorMaximal FunctionHomogeneous TypeBessel PotentialFinite NormThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.