On the order of convolution consistence of certain classes of harmonic functions with varying arguments

Abstract

"Making use of a modi ed Hadamard product or convolution of harmonic functions with varying arguments, combined with an integral operator, we study when these functions belong to a given class. Following an idea of U. Bednarz and J. Sokol we de ne the order of convolution consistence of three classes of functions and determine it for certain classes of harmonic functions with varying arguments de ned using a convolution operator."