Besov-type spaces on R and integrability for the Dunkl transform.
Abdelkefi, Chokri, Anker, Jean-Philippe, Sassi, Feriel, Sifi, Mohamed (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Abdelkefi, Chokri, Anker, Jean-Philippe, Sassi, Feriel, Sifi, Mohamed (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Mejjaoli, Hatem (2006)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: Primary 35R10, Secondary 44A15 We establish an analogue of Beurling-Hörmander’s theorem for the Dunkl-Bessel transform FD,B on R(d+1,+). We deduce an analogue of Gelfand-Shilov, Hardy, Cowling-Price and Morgan theorems on R(d+1,+) by using the heat kernel associated to the Dunkl-Bessel-Laplace operator.
Miloud Assal, Hacen Ben Abdallah (2005)
Annales mathématiques Blaise Pascal
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In this paper we study generalized Besov type spaces on the Laguerre hypergroup and we give some characterizations using different equivalent norms which allows to reach results of completeness, continuous embeddings and density of some subspaces. A generalized Calderón-Zygmund formula adapted to the harmonic analysis on the Laguerre Hypergroup is obtained inducing two more equivalent norms.
Südland, Norbert, Baumann, Gerd (2004)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 44A05, 46F12, 28A78 We prove that Dirac’s (symmetrical) delta function and the Hausdorff dimension function build up a pair of reciprocal functions. Our reasoning is based on the theorem by Mellin. Applications of the reciprocity relation demonstrate the merit of this approach.
Trimèche, Khalifa (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Mejjaoli, Hatem, Trimèche, Khalifa (2007)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 42B10 In this paper, we establish real Paley-Wiener theorems for the Dunkl transform on R^d. More precisely, we characterize the functions in the Schwartz space S(R^d) and in L^2k(R^d) whose Dunkl transform has bounded, unbounded, convex and nonconvex support.
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.
Kamoun, Lotfi (2005)
Fractional Calculus and Applied Analysis
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2000 Mathematics Subject Classification: 42B10, 43A32. In this paper we take the strip KL = [0, +∞[×[−Lπ, Lπ], where L is a positive integer. We consider, for a nonnegative real number α, two partial differential operators D and Dα on ]0, +∞[×] − Lπ, Lπ[. We associate a generalized Fourier transform Fα to the operators D and Dα. For this transform Fα, we establish an Lp − Lq − version of the Morgan's theorem under the assumption 1 ≤ p, q ≤ +∞.
Stepanov, V.D., Ushakova, E.P. (2010)
Banach Journal of Mathematical Analysis [electronic only]
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Mironova, Yu.N. (2002)
Sibirskij Matematicheskij Zhurnal
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