Abstract
Bounded Bergman projections \(P_\omega:L_\omega^p(v)\rightarrow{L_\omega^p(v)}\), induced by reproducing kernels admitting the representation
and the corresponding (1,1)-inequality are characterized in terms of Bekollé-Bonami-type conditions. The two-weight inequality for the maximal Bergman projection \(P_\omega^+:L_\omega^p(u)\rightarrow{L_\omega^p(v)}\) in terms of Sawyer-testing conditions is also discussed.
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This research was supported in part by the Ramón y Cajal program of MICINN (Spain); by Ministerio de Economía y Competitivivad, Spain, project MTM2014-52865-P; by La Junta de Andalucía, (FQM210) and (P09-FQM-4468); by Academy of Finland project no. 268009, and by Faculty of Science and Forestry of University of Eastern Finland project no. 930349; by National Science Foundation Grants DMS # 1560955 and # 1603246.
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Peláez, J.Á., Rättyä, J. & Wick, B.D. Bergman projection induced by kernel with integral representation. JAMA 138, 325–360 (2019). https://doi.org/10.1007/s11854-019-0035-5
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DOI: https://doi.org/10.1007/s11854-019-0035-5