Two weight inequality for Bergman projection

2014/06/11 by Peláez, José Ángel, Rättyä, Jouni · 3 citations
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1406.2857

Abstract

The motivation of this paper comes from the two weight inequality ‖P_ω(f)‖_L^pv≤ C‖f‖_L^pv, f∈ L^p_v, for the Bergman projection P_ω in the unit disc. We show that the boundedness of P_ω on L^p_v is characterized in terms of self-improving Muckenhoupt and Bekollé-Bonami type conditions when the radial weights v and ω admit certain smoothness. En route to the proof we describe the asymptotic behavior of the L^p-means and the L^p_v-integrability of the reproducing kernels of the weighted Bergman space A²_ω.

Cited by

• Strong and weak-type estimates for radial weighted Bergman projections
• Bergman Projections, Kernel p-Norm Estimates, and Toeplitz Operators with Békollé and Bonami weights
• Duality of mixed norm spaces induced by radial one-sided doubling weight

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