On the deformed Besov-Hankel spaces

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.