RT Journal Article
T1 Bergman projection on Lebesgue space Induced by doubling weight
A1 Peláez-Márquez, José Ángel
A1 De la Rosa, Elena
A1 Rättyä, Jouni
K1 Análisis matemático
K1 Álgebra
K1 Pesos y medidas
K1 Medida - Teoría de la
AB Let ω and ν be radial weights on the unit disc of the complexplane, and denote σ = ωp′ν− p′p and ωx = ∫ 10 sxω(s) ds for all 1 ≤ x < ∞.Consider the one-weight inequality‖Pω (f )‖Lpν ≤ C‖f ‖Lpν , 1 < p < ∞, (†)for the Bergman projection Pω induced by ω. It is shown that the momentconditionDp(ω, ν) = supn∈N∪{0}(νnp+1) 1p (σnp′+1) 1p′ω2n+1< ∞is necessary for (†) to hold. Further, Dp(ω, ν) < ∞ is also sufficient for(†) if ν admits the doubling properties sup0≤r<1∫ 1r ν(s)s ds∫ 11+r2ν(s)s ds < ∞ andsup0≤r<1∫ 1r ν(s)s ds∫ 1− 1−rKr ν(s)s ds< ∞ for some K > 1. In addition, an analogousresult for the one weight inequality ‖Pω (f )‖Dpν,k ≤ C‖f ‖Lpν , where‖f ‖pDpν,k=k−1∑j=0|f (j)(0)|p +∫D|f (k)(z)|p(1 − |z|)kpν(z) dA(z) < ∞, k ∈ N,is established. The inequality (†) is further studied by using the necessarycondition Dp(ω, ν) < ∞ in the case of the exponential type weights ν(r) =exp(− α(1−rl)β)and ω(r) = exp(−  ̃α(1−r ̃l)  ̃β), where 0 < α,  ̃α, l,  ̃l < ∞and 0 < β,  ̃β ≤ 1
PB Springer Nature
YR 2023
FD 2023-11-28
LK https://hdl.handle.net/10630/28800
UL https://hdl.handle.net/10630/28800
LA eng
NO Peláez, J.Á., de la Rosa, E. & Rättyä, J. Bergman Projection on Lebesgue Space Induced by Doubling Weight. Results Math 79, 27 (2024). https://doi.org/10.1007/s00025-023-02048-5
NO Funding for open Access charge: Universidad de Málaga / CBUAThis research was supported in part by Ministerio de Ciencia e Innovaci ́on, projectPID2022–136619NB-100; La Junta de Andaluc ́ıa, project FQM210.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 30 ene 2026