Strong and weak-type estimates for radial weighted Bergman projections

2026/07/27 by Yuerang Li, Zipeng Wang
#math.CV #math.FA

paper · pdf

Abstract

We completely characterize the L^p-boundedness and the weak-type (1,1) estimate of radial weighted Bergman projections on the unit disk. Our result, in particular, confirms a conjecture proposed by Peláez and Rättyä in 2021 and thereby settles a longstanding problem in the area that was formally posed by Dostanić in 2004. Consequently, we establish the dichotomy that a radial weighted Bergman projection is bounded either only for p=2, or for all p∈(1,∞).

Citations

• Weighted estimates for the Bergman projection on planar domains
• Around L¹ (un)boundedness of Bergman and Szegö projections
• Bergman projection induced by radial weight
• Bergman projection induced by kernel with integral representation
• Small weighted Bergman spaces
• Two weight inequality for Bergman projection
• Boundedness of the Bergman projection on L^p spaces with exponential weights
• A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa

Related

• Bergman projection induced by radial weight
• L^p Regularity of Weighted Bergman Projections
• Radial two weight inequality for maximal Bergman projection induced by a regular weight
• Two weight inequality for Bergman projection
• On the Bergman projections acting on L^∞ in the unit ball \mathbb B_n