ON ESTIMATES FOR THE GENERALIZED DUNKL TRANSFORM AND TITCHMARSH'S THEOREM IN THE SPACE $L^{p}_{\alpha,Q}(\mathbb{R}), (1
Abstract
In this paper, we study two estimates useful in applications are proved for the generalized Dunkl tranform in the space $L^{p}_{\alpha,Q}(\mathbb{R})$ where $1<p\leq2$ and $\alpha>\frac{-1}{2}$, as applied to some classes of functions characterized by a generalized modulus of continuity and we extend two interesting E.C. Titchmarsh's theorems with the higher order at same space.
Keywords
Full Text:
PDFReferences
V. A. Abilov and F. V. Abilova, Approximation of Functions by Fourier-Bessel Sums, Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 3-9 (2001).
V.A.Abilov, F.V.Abilova and M.K.Kerimov, Some Remarks Concerning the Fourier Transform in the Space L2(R) Zh. Vychisl. Mat. Mat. Fiz. 48, 939-945 (2008) [Comput. Math. Math. Phys. 48, 885-891].
V.A.Abilov, F.V.Abilova and M.K.Kerimov, Some Remarks Concerning the Fourier Transform in the Space L2(Rn), Zhurnal Vychislitel'noi Matematiki iMatematicheskoi Fiziki, 2008, Vol. 48 No. 12, pp. 2113-2120.
E. A. Al Zahrani and M. A. Mourou, The continuous wavelet transform associated with a Dunkl type operator on the real line, Advances in Pure Mathematics, 2013, Vol. 3, pp. 443-450.
M. Boujeddaine, R. Daher and M. El Hamma, Sobolev Spaces for the Dunkl operator on the real line, Asia Pacic Journal of Mathematics, Vol. 1, No. 3 (2014) pp. 176-181.
M. El Hamma and R. Daher, Growth properties of the Dunkl Transform on the real line, Int. Journal of Math. Analysis, Vol. 6, No. 44 (2012) pp. 2173-2177.
M. EL Hamma, R. Daher and M. Boujeddaine, On estimates for the Dunkl transform in the space Lp(R; jxj2+1dx), Nonlinear Studies, 2014, Vol. 21, No. 3 pp.435-441.
M. El Hamma and R. Daher, On Estimates for the Dunkl transform in the space L2;(R), Int. J. Analysis and Applications. Vol. 6, No. 1 (2014), pp. 53-62.
M. El Hamma and R. Daher, On Estimates for the Dunkl transform in the space L2;(R), Int. J. Analysis and Applications. Vol. 6, No. 1 (2014), pp. 53-62.
M. El Hamma and R. Daher, Genaralization of Titchmarsh 's theorem for the Dunkl transform on the real line On Estimates for the Dunkl transform, Analele Universitatii de Vest, Timisoara, Seria Matematica- Informatica, LI, 2 (2013), 47-55.
E. C. Titchmarsh, Introduction to the theory of Fourier Integrals, Oxford University Press, Amen House, London, E. C. 4, 1948.
DOI: https://doi.org/10.22190/FUMI200921004A
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)