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Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

Gasmi, A.Sifi, M.Soltani, F. — 2006

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35 We introduce some new weighted Herz spaces associated with the Dunkl operator on R. Also we characterize by atomic decompositions the corresponding Herz-type Hardy spaces. As applications we investigate the Dunkl transform on these spaces and establish a version of Hardy inequality for this transform. * The authors are supported by the DGRST research project 04/UR/15-02.

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