On the deformed besov-hankel spaces

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.