Bergman projection induced by kernel with integral representation

2016/06/02 by Peláez, José A., Rättyä, Jouni, Wick, Brett D. · 1 citation
#Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.00718

Abstract

Bounded Bergman projections P_ω:L^p_ω(v)→ L^p_ω(v), induced by reproducing kernels admitting the representation \frac1(1-zζ)^γ∫₀¹\fracdν(r)1-rzζ, 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⁺_ω:L^p_ω(u)→ L^p_ω(v) in terms of Sawyer-testing conditions is also discussed.

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