2019/07/24 by Peláez, José Ángel, Rättyä, Jouni · 1 citation
#Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1907.10563
A radial weight ω belongs to the class \widehatD if there exists C=C(ω)≥ 1 such that ∫r1 ω(s) ds≤ C∫(1+r)/(2)1ω(s) ds for all 0≤ r<1. Write ω∈\checkD if there exist constants K=K(ω)>1 and C=C(ω)>1 such that \widehatω(r)≥ C\widehatω(1-(1-r)/(K)) for all 0≤ r<1. In a recent paper, we have recently prove that these classes of radial weights arise naturally in the operator theory of Bergman spaces induced by radial weights. Classical results by Hardy and Littlewood, and Shields and Williams, show that the weighted Bergman space of harmonic functions is not closed by harmonic conjugation if ω∈\widehatD∖ \checkD and 0