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Acta Mathematica Vietnamica

Finite Decomposition of Herz-Type Hardy Spaces for the Dunkl Operator

icon-email Mehdi Lachiheb

Abstract

The corresponding Herz-type Hardy spaces to new weighted Herz spaces HKα,qβ,p associated with the Dunkl operator on R have been characterized by atomic decompositions. Later a new characterization of HKα,qβ,p on the real line is introduced. This helped us in the work to characterize that the norms of the Herz-type Hardy spaces for the Dunkl Operator can be achieved by finite central atomic decomposition in some dense subspaces of them. Secondly, as an application we prove that a sublinear operator satisfying many conditions can be uniquely extended to a bounded operator in the Herz-type Hardy spaces for the Dunkl Operator.