Abstract
We provide a new characterization for Carleson measures in terms of the \(L^p({\mathbb {S}}_n)\) norms of certain functions in admissible approach regions on the unit ball of \({\mathbb {C}}^n\). Some of the tools used in the proof for one dimensional case are not available for higher dimensions, such as Calderón-Zygmund decomposition. Our approach involves a duality argument and maximal functions of \(L^p({\mathbb {S}}_n)\) functions on the unit ball of \({\mathbb {C}}^n\). We also show some applications of our main results to Riemann–Stieltjes integral operators.
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Xiaosong Liu is in part supported by NNSF of China (Nos. 11701222, 11801347), China Postdoctoral Science Foundation (No. 2018M633090). Zengjian Lou is in part supported by NNSF of China (Nos. 12071272, 11871293) and Department of Education of Guangdong Province (2018KZDXM034). Ruhan Zhao is in part supported by the NNSF of China (No. 117201003).
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Liu, X., Lou, Z. & Zhao, R. A New Characterization of Carleson Measures on the Unit Ball of \({\mathbb {C}}^n\). Integr. Equ. Oper. Theory 93, 51 (2021). https://doi.org/10.1007/s00020-021-02667-z
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DOI: https://doi.org/10.1007/s00020-021-02667-z