ON THE SOLID HULL OF THE HARDY--LORENTZ SPACE
Miroljub Jevtić, Miroslav Pavlović (2009)
Publications de l'Institut Mathématique
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Miroljub Jevtić, Miroslav Pavlović (2009)
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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.
Samko, Stefan (2005)
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Mathematics Subject Classification: 26D10. The sharp constant is obtained for the Hardy-Stein-Weiss inequality for fractional Riesz potential operator in the space L^p(R^n, ρ) with the power weight ρ = |x|^β. As a corollary, the sharp constant is found for a similar weighted inequality for fractional powers of the Beltrami-Laplace operator on the unit sphere.
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