Some constructive criteria of optimal embeddings for potentials

Abstract

In this article, we study the spaces of potentials in n-dimensional Euclidean space. They are constructed on the basis of rearrangement invariant spaces (RISs) by means of convolutions with kernels of general forms. We establish the constructive criteria for embeddings of potentials in RISs and describe explicitly optimal RISs for such embeddings.

Keywords:

• convolution
• rearrangement invariant space
• weighted Lorentz space
• cone of rearrangements
• space of potentials

AMS Subject Classifications::

• 42B35
• 43A15
• 43A80
• 47H50

Acknowledgement

This study was supported by the Russian Foundation for Basic Research (project nos. 09-01-00093 and 08-01-00443).