On the deformed besov-hankel spaces

Salem Ben Saïd; Mohamed Amine Boubatra; Mohamed Sifi

doi:10.7494/OpMath.2020.40.2.171

On the deformed besov-hankel spaces

Salem Ben Saïd, Mohamed Amine Boubatra, Mohamed Sifi

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this paper we introduce function spaces denoted by BH^p,r _κ,β (0 < β < 1, 1 ≤ p,r ≤ +∞) as subspaces of L^p that we call deformed Besov-Hankel spaces. We provide characterizations of these spaces in terms of Bochner-Riesz means in the case 1 ≤ p ≤ +∞ and in terms of partial Hankel integrals in the case 1 < p < +∞ associated to the deformed Hankel operator by a parameter κ > 0. For p = r = +∞, we obtain an approximation result involving partial Hankel integrals.

Original language	English
Pages (from-to)	171-207
Number of pages	37
Journal	Opuscula Mathematica
Volume	40
Issue number	2
DOIs	https://doi.org/10.7494/OpMath.2020.40.2.171
Publication status	Published - 2020

Keywords

Besov spaces
Bochner-Riesz means
Deformed Hankel kernel
Partial Hankel integrals

ASJC Scopus subject areas

Mathematics(all)

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10.7494/OpMath.2020.40.2.171

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AU - Ben Saïd, Salem

AU - Boubatra, Mohamed Amine

AU - Sifi, Mohamed

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AB - In this paper we introduce function spaces denoted by BHp,r κ,β (0 < β < 1, 1 ≤ p,r ≤ +∞) as subspaces of Lp that we call deformed Besov-Hankel spaces. We provide characterizations of these spaces in terms of Bochner-Riesz means in the case 1 ≤ p ≤ +∞ and in terms of partial Hankel integrals in the case 1 < p < +∞ associated to the deformed Hankel operator by a parameter κ > 0. For p = r = +∞, we obtain an approximation result involving partial Hankel integrals.

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KW - Bochner-Riesz means

KW - Deformed Hankel kernel

KW - Partial Hankel integrals

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On the deformed besov-hankel spaces

Abstract

Keywords

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