Abstract
In this paper, we completely characterize the positive Borel measures μ on the unit ball \({\mathbb{B}_n}\) such that the differential type operator \({{\cal R}^m}\) of order m ∈ ℕ is bounded from Hardy type tent space \({\cal H}{\cal T}_{q,\alpha}^p({\mathbb{B}_n})\) into Ls(μ) for full range of p, q, s, α. Subsequently, the corresponding compact description of differential type operator \({{\cal R}^m}\) is also characterized. As an application, we obtain the boundedness and compactness of integration operator Jg from \({\cal H}{\cal T}_{q,\alpha}^p({\mathbb{B}_n})\) to \({\cal H}{\cal T}_{s,\beta}^t({\mathbb{B}_n})\), and the methods used here are adaptable to the Hardy spaces.
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Supported by National Natural Science Foundation of China (Grant No. 11771340)
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Wang, M.F., Zhou, L. Embedding Derivatives and Integration Operators on Hardy Type Tent Spaces. Acta. Math. Sin.-English Ser. 38, 1069–1093 (2022). https://doi.org/10.1007/s10114-022-0405-2
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DOI: https://doi.org/10.1007/s10114-022-0405-2