Modulus of Continuity and Modulus of Smoothness related to the Deformed Hankel Transform

In this paper, we consider the deformed Hankel transform F κ , which is a deformation of the Hankel transform by a parameter κ > 1 4 . We introduce, via modulus of continuity, a function subspace of L p ( d μ κ ) that we call deformed Hankel Dini–Lipschitz spaces. In the case p = 2 , we provide e...

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Bibliographic Details
Published in:Resultate der Mathematik 2021-08, Vol.76 (3), Article 164
Main Authors: Negzaoui, Selma, Oukili, Sara
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:In this paper, we consider the deformed Hankel transform F κ , which is a deformation of the Hankel transform by a parameter κ > 1 4 . We introduce, via modulus of continuity, a function subspace of L p ( d μ κ ) that we call deformed Hankel Dini–Lipschitz spaces. In the case p = 2 , we provide equivalence theorem: we get a characterization of those spaces by means of asymptotic estimate growth of the norm of their F κ transform for 0 < γ < 1 and α ≥ 0 . As a consequence we have the analogous of generalized Titchmarsh theorem in L 2 ( d μ κ ) . Moreover, we introduce the modulus of smoothness related to F κ for which we study some properties on the Sobolev type space.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-021-01474-7