Abstract
This paper deals with the symmetric space of functions and its subspace where continuous functions are dense is considered. Main properties of convolution which plays a vital role in harmonic analysis, as in other areas of mathematics are established in this space. Following the classical case, it is proved that the convolution can be approximated by linear combinations of shifts in a subspace of the considered space. An approximate identity for the convolution is also considered in that subspace.
Highlights
Main properties of convolution which plays a vital role in harmonic analysis, as in other areas of mathematics are established in this space
An approximate identity for the convolution is considered in that subspace
Convolution operation plays a vital role in harmonic analysis, as in other areas of mathematics
Summary
Convolution operation plays a vital role in harmonic analysis, as in other areas of mathematics. To have knowledge of basic properties of convolution in various Banach function spaces is very important and useful in the study of the problems of harmonic analysis, approximation theory, theory of partial di¤erential equations, etc. In [12, 16, 23], an analogue of the classical Young inequality and some properties of the convolution of periodic functions belonging to Morrey type spaces have been obtained. In [12], it was proved that the convolution in the subspace of Morrey space can be approximated by ...nite linear combinations of shifts.
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