The paper presents a method for establishing direct and strong converse inequalities in terms of K-functionals for convolution operators acting in homogeneous Banach spaces of multivariate functions. The method is based on the behaviour of the Fourier transform of the kernel of the convolution operator. AMS classification: 41A25, 41A27, 41A35, 41A36, 41A40, 41A63, 41A65, 42A10, 42A38, 42A45, 42...

We consider operators of convolution generated by L func tions in L and various spaces of almost periodic functions It turns out to be that if such an operator is invertible in one of these spaces then it is in vertible in all the spaces we consider Further we prove that any convolution has identical norms in many natural couples of functional spaces

The classical theory of Hardy spaces on n has received an important impetus from the work of Fefferman and Stein, Lu and Yang 1, 2 . Their work resulted in many applications involving sharp estimates for convolution and multiplier operators. By using the technique of Herz-type Hardy spaces for the Dunkl operator Λα, we are attempting in this paper to study the Dunkl convolution operators, andwe...

In this paper it is shown how false operator responses due to missing or uncertain data can be significantly reduced or eliminated. Perhaps the most well-known of such effects are the various ‘edge effects’ which invariably occur at the edges of the input data set. Further, it is shown how operators having a higher degree of selectivity and higher tolerance against noise can be constructed usin...

We survey some known results about generator property of operator matrices with diagonal or coupled domain. Further, we use basic properties of the convolution of operator-valued mappings in order to obtain stability results for such semigroups. 1. Operator matrices with diagonal domain While tackling abstract problems that are related to concrete initial–boundary value problems with dynamical ...