Abstract
We prove that the weighted Bergman projection \(P_\gamma \) is a bounded operator on the weighted Lebesgue space \(L^p(\Omega , r(x)^\lambda \mathrm{{d}}m(x))\) for a certain range of parameters p, \(\gamma \) and \(\lambda \). Here \(\Omega \) is a bounded domain in \(\mathbb R^n\) with smooth boundary. This result is used to prove boundedness of \(P_\gamma \) acting on weighted mixed norm space \(L^{p,q}_\alpha (\Omega )\), again assuming certain conditions on the parameters. We describe the dual of harmonic mixed norm space \(B^{p,q}_\alpha (\Omega )\) for a certain range of parameters.
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The authors thank the anonymous referee for the careful reading of the manuscript and for spotting a difference between cases \(p \le q\) and \(p > q\) in Theorem 3.2.
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Communicated by Kehe Zhu.
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Arsenović, M., Savković, I. Bergman projections on weighted mixed norm spaces and duality. Ann. Funct. Anal. 13, 70 (2022). https://doi.org/10.1007/s43034-022-00217-1
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DOI: https://doi.org/10.1007/s43034-022-00217-1