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The boundedness of the generalized anisotropic potentials with rough kernels in the Lorentz spaces.
- Source :
-
Integral Transforms & Special Functions . Dec2011, Vol. 22 Issue 12, p919-935. 17p. - Publication Year :
- 2011
-
Abstract
- In this paper, we study the generalized anisotropic potential integral K α, γ⊗ f and anisotropic fractional integral I Ω,α, γ f with rough kernels, associated with the Laplace–Bessel differential operator Δ B . We prove that the operator f→K α, γ⊗ f is bounded from the Lorentz spaces to for 1≤p<q≤∞, 1≤r≤s≤∞. As a result of this, we get the necessary and sufficient conditions for the boundedness of I Ω,α, γ from the Lorentz spaces to , 1<p<q<∞, 1≤r≤s≤∞ and from to , 1<q<∞, 1≤r≤∞. Furthermore, for the limiting case p=Q/α, we give an analogue of Adams’ theorem on the exponential integrability of I Ω,α, γ in . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10652469
- Volume :
- 22
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Integral Transforms & Special Functions
- Publication Type :
- Academic Journal
- Accession number :
- 67043605
- Full Text :
- https://doi.org/10.1080/10652469.2010.548334