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

Abstract

In this article, we study the spaces of potentials is n -dimensional Euclidean space. They constructed on the basis of rearrangement - invariant spaces (RISs) by means of convolutions with kernels of general form. In particular included in the consideration, the classical spaces of potentials of Bessel and Riesz. For them, the criteria for embedding in the RIS are found, and explicit descriptions of the optimal RIS for these embeddings are obtained in the case of the basic weight Lorentz space.