Analogs of <i>S</i>-type spaces of partially even functions

Abstract

We construct analogs of $S$-type spaces whose elements are functions that are even in a part of components of their arguments. We obtain a formula that expresses a power of a Bessel operator via the corresponding powers of a differential operator. This formula enables us to establish a relation between these spaces in terms of the Fourier – Bessel transformation and to clarify some basic properties of typical operations on their elements.