Author： Guliev V.S.
Publisher： Springer Publishing Company
ISSN： 0133-3852
Source： Analysis Mathematica, Vol.26, Iss.2, 2000-01, pp. : 99-118
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Abstract
The Hardy-Littlewood-Bessel maximal functions (B-maximal functions), Morrey-Bessel and BMO-Bessel spaces were introduced and studied in [6]. In the present paper, we study the anisotropic Riesz-Bessel potential (B-potential) in the Morrey-Bessel and BMO-Bessel spaces. We obtain a theorem analogous to the Sobolev theorem, for the anisotropic Riesz-Bessel potential in Morrey-Bessel spaces. We introduce a metric characteristic Ω_p, in the space of locally integrable functions and establish estimates connecting the characteristics of the image and preimage of the corresponding integral transform. These estimates are of independent interest. Moreover, they are used for the investigation of integral operators in different scales of Banach function spaces, in particular, in weighted L_p^-spaces. The results seem to be new even in the isotropic case.
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