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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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