Muckenhoupt-Type Weights and Quantitative Weighted Estimate in the Bessel Setting

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 Lᵖw if and only if w is in the class A₏,. We introduce a new class of Muckenhoupt-type weights A₏, in the Bessel setting, which is different from A₏, but characterizes the weighted boundedness for the Hardy--Littlewood maximal operators. We also establish the weighted Lᵖ boundedness and compactness, as well as the endpoint weak type boundedness of Riesz commutators. The quantitative weighted bound is also established.