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Bergman projection induced by kernel with integral representation

  • José Ángel Peláez
  • Jouni Rättyä
  • Brett D. WickEmail author
Article
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Abstract

Bounded Bergman projections \(P_\omega:L_\omega^p(v)\rightarrow{L_\omega^p(v)}\), induced by reproducing kernels admitting the representation
$$\frac{1}{(1-\overline{z}\zeta)^\gamma}\int_{0}^{1} \frac{dv(r)}{1-r\overline{z}\zeta},\;\;0\leq{r}<1,$$
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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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  • José Ángel Peláez
    • 1
  • Jouni Rättyä
    • 2
  • Brett D. Wick
    • 3
    Email author
  1. 1.Departamento de Análisis MatemáticoUniversidad de MálagaMálagaSpain
  2. 2.University of Eastern FinlandJoensuuFinland
  3. 3.Department of MathematicsWashington University — St. LouisSt. LouisUSA

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