$L^p$ estimates for the Bergman projection on some Reinhardt domains

The Bergman Kernel Function of Some Reinhardt Domains

The boundary behavior of the Bergman Kernel function of some Reinhardt domains is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points (z, z̄). Let D be the Reinhardt domain D = { z ∈ C | ‖z‖α = n ∑

The Bergman Projection on Sectorial Domains

Lp error estimates for projection approximations

We provide an error estimate for the local mean projection approximation in L p([0, τ∗]) for p ∈ [1,+∞[, in terms of the regularity of the underlying grid, and we apply it to the corresponding projection approximation of weakly singular Fredholm integral equations of the second kind. © 2004 Elsevier Ltd. All rights reserved.

Analytic Functionals and the Bergman Projection on Circular Domains

A property of the Bergman projection associated to a bounded circular domain containing the origin in C^ is proved: Functions which extend to be holomorphic in large neighborhoods of the origin are characterized as Bergman projections of smooth functions with small support near the origin. For certain circular domains D, it is also shown that functions which extend holomorphically to a neighbor...

The Bergman Kernel and Projection on Non-smooth Worm Domains

We study the Bergman kernel and projection on the worm domains Dβ = { ζ ∈ C : Re ( ζ1e −i log |ζ2| 2) > 0, ∣∣ log |ζ2| ∣∣ < β − π 2 } and D β = { z ∈ C : ∣Im z1 − log |z2| ∣∣ < π 2 , | log |z2| | < β − π 2 } for β > π. These two domains are biholomorphically equivalent via the mapping D β ∋ (z1, z2) 7→ (e z1 , z2) ∋ Dβ . We calculate the kernels explicitly, up to an error term that can be contr...