Muckenhoupt-type weights and quantitative weighted estimates in the bessel setting
Journal
Mathematische Zeitschrift
Journal Volume
309
Journal Issue
1
ISSN
0025-5874
1432-1823
Date Issued
2024-11-28
Author(s)
Abstract
Part of the intrinsic structure of singular integrals in the Bessel setting is captured by Muckenhoupt-type weights. Anderson–Kerman showed that the Bessel Riesz transform is bounded on weighted Lwp if and only if w is in the class Ap,λ. We introduce a new class of Muckenhoupt-type weights A~p,λ in the Bessel setting, which is different from Ap,λ but characterizes the weighted boundedness for the Hardy–Littlewood maximal operators. We first investigate the quantitative weighted estimates with respect to the new weights A~p,λ for the sparse operators, the standard one and the one associated to the Bessel BMO space. Then via these sparse operators and the median value technique, we establish the (quantitative) weighted Lp boundedness and compactness, as well as the endpoint weak type boundedness of Riesz transform commutators.
SDGs
Publisher
Springer Science and Business Media LLC
Type
journal article