Sharp Békollé estimates for the Bergman projection

A Sharp Norm Estimate of the Bergman Projection on L Spaces

We show that the norm of the Bergman projection on L of the unit ball in C is comparable to csc(π/p) for 1 < p <∞.

The Bergman Projection on Sectorial Domains

Sharp Estimates for the Arithmetic Nullstellensatz

We present sharp estimates for the degree and the height of the polynomials in the Nullstellensatz over the integer ring Z. The result improves previous work of P. Philippon, C. Berenstein and A. Yger, and T. Krick and L. M. Pardo. We also present degree and height estimates of intrinsic type, which depend mainly on the degree and the height of the input polynomial system. As an application we ...

$L^p$ boundedness of the Bergman projection on some generalized Hartogs triangles

‎In this paper we investigate a two classes of domains in $mathbb{C}^n$ generalizing the Hartogs triangle‎. ‎We prove optimal estimates for the mapping properties of the Bergman projection on these domains.

Sharp Morawetz Estimates

We prove sharp Morawetz estimates – global in time with a singular weight in the spatial variables – for the linear wave, Klein–Gordon and Schrödinger equations, for which we can characterise the maximisers. We also prove refined inequalities with respect to the angular integrability.