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On the deformed Besov-Hankel spaces

Said Salem Ben, Boubatra Mohamed Amine, Sifi Mohamed

Opuscula Mathematica

2020

Vol. 40, no. 2

171--207

In this paper we introduce function spaces denoted by [formula] 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 k > 0. For p = r = +∞, we obtain an approximation result involving partial Hankel integrals.