Displaying similar documents to “Structure of the Hardy operator related to Laguerre polynomials and the Euler differential equation.”

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

Gasmi, A., Sifi, M., Soltani, F. (2006)

Fractional Calculus and Applied Analysis

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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.

Best Constant in the Weighted Hardy Inequality: The Spatial and Spherical Version

Samko, Stefan (2005)

Fractional Calculus and Applied Analysis

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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.