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arXiv · 2405.01081

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

Ji Li·Chong-Wei Liang·Chun-Yen Shen·Brett D. Wick
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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 $A_{p,\lambda}$. We introduce a new class of Muckenhoupt-type weights $\widetilde A_{p,\lambda}$ in the Bessel setting, which is different from $A_{p,\lambda}$ 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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Ji Li, Chong-Wei Liang, Chun-Yen Shen, Brett D. Wick. 2024-05-02. Muckenhoupt-Type Weights and Quantitative Weighted Estimate in the Bessel Setting. https://arxiv.org/abs/2405.01081

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