Convolution Operators and Bochner-Riesz Means on Herz-Type Hardy Spaces in the Dunkl Setting

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 establish a version of multiplier theorem for the maximal Bochner-Riesz operators on these spaces. The Dunkl operator Λα, α > −1/2, associated with the reflection group 2 on :