Geodesic
Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line
Fractional calculus and applied analysis, Tome 9 (2006) no. 3, pp. 287-306

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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.
Keywords: Dunkl Operator, Dunkl Kernel, Dunkl Transform, Dunkl Translation Operators, Herz-Type Hardy Spaces, Atomic Decompositions, 46F12, 44A15, 44A35 
Gasmi, A.; Sifi, M.; Soltani, F. Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line. Fractional calculus and applied analysis, Tome 9 (2006) no. 3, pp. 287-306. http://geodesic.mathdoc.fr/item/FCAA_2006_9_3_a5/
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     author = {Gasmi, A. and Sifi, M. and Soltani, F.},
     title = {Herz-Type {Hardy} {Spaces} for the {Dunkl} {Operator} on the {Real} {Line}},
     journal = {Fractional calculus and applied analysis},
     pages = {287--306},
     year = {2006},
     volume = {9},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/FCAA_2006_9_3_a5/}
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