Optimal embeddings of Bessel and Riesz type potentials on the basis of weighted Lorentz spaces

Gulden Karshygina

2017

Data confidence 70 medium

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Abstract

We study a space of potentials on the n-dimensional Euclidean space. They are constructed on the basis of rearrangement invariant spaces (RISs) by means of convolutions with kernels of general form. In particular, the spaces of classical potentials of Bessel and Riesz are included in the discussion. We establish the integral properties of potentials. For them the criteria for embedding in the RIS are found and explicit descriptions of the optimal RIS for these embeddings are obtained in case of the basic weighted Lorentz space. The aim of this paper is to give an explicit description of the optimal RIS X(Rn) for embeddings HEG(Rn)⊂X(Rn) in the case when the base RIS E(Rn) coincides with the weighted Lorentz space Λp(u).