Abstract
It is shown in quantitative terms that the maximal Bergman projection
is bounded from \(L^{p}_{\nu }\) to \(L^{p}_{\eta }\) if and only if
provided ω,ν,η are radial regular weights. A radial weight σ is regular if it satisfies \({\sigma }(r){\asymp {\int \limits }}_{r}^{1}{\sigma }(t) dt/(1-r)\) for all 0 ≤ r < 1. It is also shown that under an appropriate additional hypothesis involving ω and η, the Bergman projection Pω and \({P}^{+}_{\omega }\) are simultaneously bounded.
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Acknowledgement
The authors would like to thank the referee for careful reading of the manuscript and for pointing out a matter which yielded the final version of Theorem 2.
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Dedicated to Fernando Pérez-González on the occasion of his retirement
This research was supported in part by Ministerio de Economía y Competitivivad, Spain, projects PGC2018-096166-B-100 and MTM2017-90584-REDT; La Junta de Andalucía, project FQM210; Academy of Finland project no. 268009.
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Korhonen, T., Peláez, J.Á. & Rättyä, J. Radial Two Weight Inequality for Maximal Bergman Projection Induced by a Regular Weight. Potential Anal 54, 561–574 (2021). https://doi.org/10.1007/s11118-020-09838-4
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DOI: https://doi.org/10.1007/s11118-020-09838-4