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Carleson measures for weighted harmonic mixed norm spaces on bounded domains in ℝn

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Abstract

We study weighted mixed norm spaces of harmonic functions defined on smoothly bounded domains in ℝn. Our principal result is a characterization of Carleson measures for these spaces. First, we obtain an equivalence of norms on these spaces. Then we give a necessary and sufficient condition for the embedding of the weighted harmonic mixed norm space into the corresponding mixed norm space.

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Acknowledgments

The author would like to thank Professor Miloš Arsenović for providing valuable suggestions during the writing of this paper. The author is also very grateful to the anonymous referee for constructive suggestions that contributed to this paper.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Banja Luka, Bulevar vojvode Stepe Stepanovića 71, Banja Luka, Bosnia and Herzegovina

    Ivana Savković

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  1. Ivana Savković
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Correspondence to Ivana Savković.

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Savković, I. Carleson measures for weighted harmonic mixed norm spaces on bounded domains in ℝn. Czech Math J 72, 1205–1216 (2022). https://doi.org/10.21136/CMJ.2022.0018-22

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