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Carleson type measures for harmonic mixed norm spaces with application to Toeplitz operators

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Abstract

Let Ω be a bounded domain in ℝn with a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q , with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q . As an application, the authors characterize the boundedness (and compactness) of Toeplitz operators T µ on h p,q for those positive finite Borel measures µ.

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Correspondence to Zhangjian Hu.

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Project supported by the National Natural Science Foundation of China (Nos. 11101139, 11271124), the Natural Science Foundation of Zhejiang Province (Nos. Y6090036, Y6100219) and the Foundation of Creative Group in Universities of Zhejiang Province (No. T200924).

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Hu, Z., Lv, X. Carleson type measures for harmonic mixed norm spaces with application to Toeplitz operators. Chin. Ann. Math. Ser. B 34, 623–638 (2013). https://doi.org/10.1007/s11401-013-0776-x

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  • DOI: https://doi.org/10.1007/s11401-013-0776-x

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2000 MR Subject Classification

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