TY  - JOUR
ID  - BenSaïd2020
LB  - BenSaïd2020
AU  - Ben Saïd, Salem
AU  - Amine Boubatra, Mohamed
AU  - Sifi, Mohamed
TI  - On the deformed Besov-Hankel spaces
ST  - On the deformed Besov-Hankel spaces
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 2
SP  - 171
EP  - 207
DO  - https://doi.org/10.7494/OpMath.2020.40.2.171
UR  - https://doi.org/10.7494/OpMath.2020.40.2.171
AB  - 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.
KW  - deformed Hankel kernel
KW  - Besov spaces
KW  - Bochner-Riesz means
KW  - partial Hankel integrals
SN  - 1232-9274
ER  -