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Bessel (Riesz) potentials on banach function spaces and their applications I theory

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Abstract

In this paper, we shall introduce the concept of the Bessel (Riesz) potential Köthe function spacesX s (X s) and give some dual estimates for a class of operators determined by a semi-group in the spacesL q (−T, T; X s) (L q(−T, T; X s)). Moreover, some time-spaceL p −L p′ estimates for the semi-group exp(it(-Δ)m/2) and the operatorA:=∫ t0 exp(i(t-τ)(-Δ)m/2)·dτ in the Lebesgue-Besov spacesL q (−T,T;B s p,2 are given. On the basis of these results, in a subsequent paper we shall present some further applications to a class of nonlinear wave equations.

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Authors and Affiliations

  1. Department of Mathematics, Hebei University, 071002, Baoding, China

    Wang Baoxiang

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  1. Wang Baoxiang
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Supported in part by the Doctoral Research Foundation of Hebei Province

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Baoxiang, W. Bessel (Riesz) potentials on banach function spaces and their applications I theory. Acta Mathematica Sinica 14, 327–340 (1998). https://doi.org/10.1007/BF02580436

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  • DOI: https://doi.org/10.1007/BF02580436

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