Hulls and kernels of function classes and behavior of the Fourier transform
by
Archil Gulisashvili
Department of Mathematics, Ohio University, Athens, OH 45701

We find the rearrangement-invariant, equimodular, and solid hulls and kernels of some function classes on n-dimensional Euclidean space Rⁿ. These classes consist of all functions for which the Fourier transform belongs to a given space A of tempered distributions. We consider the cases where A is the space L^p, the space L^p_loc, or the space M of compex Borel measures of locally bounded variation. We also introduce and study new function classes which arise as the hulls of some of the classes under consideration.

Date received: April 2, 1999