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RIUMA. Repositorio Institucional de la Universidad de Málaga author Peláez-Márquez, José Ángel author De la Rosa, Elena author Rättyä, Jouni 2024-01-17T08:11:26Z 2024-01-17T08:11:26Z 2023-11-28 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 https://hdl.handle.net/10630/28800 10.1007/s00025-023-02048-5 Let ω and ν be radial weights on the unit disc of the complex plane, and denote σ = ωp′ ν− p′ p and ωx = ∫ 1 0 sxω(s) ds for all 1 ≤ x < ∞. Consider the one-weight inequality ‖Pω (f )‖Lp ν ≤ C‖f ‖Lp ν , 1 < p < ∞, (†) for the Bergman projection Pω induced by ω. It is shown that the moment condition Dp(ω, ν) = sup n∈N∪{0} (νnp+1) 1 p (σnp′+1) 1 p′ ω2n+1 < ∞ is necessary for (†) to hold. Further, Dp(ω, ν) < ∞ is also sufficient for (†) if ν admits the doubling properties sup0≤r<1 ∫ 1 r ν(s)s ds ∫ 1 1+r 2 ν(s)s ds < ∞ and sup0≤r<1 ∫ 1 r ν(s)s ds ∫ 1− 1−r K r ν(s)s ds < ∞ for some K > 1. In addition, an analogous result for the one weight inequality ‖Pω (f )‖Dp ν,k ≤ C‖f ‖Lp ν , where ‖f ‖p Dp ν,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 necessary condition 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 eng Atribución 4.0 Internacional Análisis matemático Álgebra Pesos y medidas Medida - Teoría de la Bergman projection on Lebesgue space Induced by doubling weight journal article 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 URL https://riuma.uma.es/bitstreams/7dd57360-b72c-4e1b-b366-cb3475be4517/download File MD5 0fa81732fe211970bb587cc2713c6b1b 434934 application/pdf s00025-023-02048-5.pdf