On estimates for weighted Bergman projections

الأصل · EN

In this note we show that the weighted L²-Sobolev estimates obtained by P. Charpentier, Y. Dupain & M. Mounkaila for the weighted Bergman projection of the Hilbert space L²(Ω,dμ₀) where Ω is a smoothly bounded pseudoconvex domain of finite type in Cⁿ and μ₀=(-ρ₀)ʳdλ, λ being the Lebesgue measure, r₊ and ρ₀ a special defining function of Ω, are still valid for the Bergman projection of L²(Ω,dμ) where μ=(-ρ)ʳdλ, ρ being any defining function of Ω. In fact a stronger directional Sobolev estimate is established. Moreover similar generalizations are obtained for weighted Lᵖ-Sobolev and lipschitz estimates in the case of pseudoconvex domain of finite type in C² and for some convex domains of finite type.