Recent zbMATH articles in MSC 46F12https://zbmath.org/atom/cc/46F122024-03-13T18:33:02.981707ZWerkzeugFinite decomposition of Herz-type Hardy spaces for the Dunkl operatorhttps://zbmath.org/1528.460292024-03-13T18:33:02.981707Z"Lachiheb, Mehdi"https://zbmath.org/authors/?q=ai:lachiheb.mehdiSummary: The corresponding Herz-type Hardy spaces to new weighted Herz spaces \(HK^{\beta, p}_{\alpha, q}\) associated with the Dunkl operator on \(\mathbb{R}\) have been characterized by atomic decompositions. Later a new characterization of \(HK^{\beta, p}_{\alpha, q}\) 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.