Opuscula Math. 40, no. 2 (2020), 171-207

Opuscula Mathematica

On the deformed Besov-Hankel spaces

Salem Ben Saïd
Mohamed Amine Boubatra
Mohamed Sifi

Abstract. In this paper we introduce function spaces denoted by \(BH_{\kappa,\beta}^{p,r}\) (\(0\lt\beta\lt 1\), \(1\leq p, r \leq +\infty\)) 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 \(1\leq p\leq +\infty\) and in terms of partial Hankel integrals in the case \(1\lt p\lt +\infty\) associated to the deformed Hankel operator by a parameter \(\kappa\gt 0\). For \(p=r=+\infty\), we obtain an approximation result involving partial Hankel integrals.

Keywords: deformed Hankel kernel, Besov spaces, Bochner-Riesz means, partial Hankel integrals.

Mathematics Subject Classification: 44A15, 46E30.

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  • Mohamed Amine Boubatra
  • ORCID iD https://orcid.org/0000-0002-3595-7246
  • Université Tunis El Manar, Faculté des Sciences de Tunis, Laboratoire d'Analyse Mathématique et Applications, LR11ES11, Campus Universitaire, 2092 El Manar I, Tunis, Tunisia
  • Mohamed Sifi (corresponding author)
  • ORCID iD https://orcid.org/0000-0003-0607-8303
  • Université Tunis El Manar, Faculté des Sciences de Tunis, Laboratoire d'Analyse Mathématique et Applications, LR11ES11, Campus Universitaire, 2092 El Manar I, Tunis, Tunisia
  • Communicated by Vicentiu D. Radulescu.
  • Received: 2019-11-11.
  • Revised: 2020-01-29.
  • Accepted: 2020-01-30.
  • Published online: 2020-03-09.
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Cite this article as:
Salem Ben Saïd, Mohamed Amine Boubatra, Mohamed Sifi, On the deformed Besov-Hankel spaces, Opuscula Math. 40, no. 2 (2020), 171-207, https://doi.org/10.7494/OpMath.2020.40.2.171

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