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

2024/05/02 by Li, Ji, Liang, Chong-Wei, Shen, Chun-Yen +1 · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.01081

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 L^p_w if and only if w is in the class A_p,λ. We introduce a new class of Muckenhoupt-type weights \widetilde A_p,λ in the Bessel setting, which is different from A_p,λ but characterizes the weighted boundedness for the Hardy--Littlewood maximal operators. We also establish the weighted L^p boundedness and compactness, as well as the endpoint weak type boundedness of Riesz commutators. The quantitative weighted bound is also established.

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