Lp estimates for the $\bar\partial$-equation on a class of infinite type domains

Abstract

We prove Lp estimates, 1 ≤ p ≤ ∞, for solutions to the Cauchy–Riemann equations [Formula: see text] on a class of infinite type domains in ℂ2. The domains under consideration are a class of convex ellipsoids, and we show that if ϕ is a [Formula: see text]-closed (0, 1)-form with coefficients in Lp and u is the Henkin kernel solution to [Formula: see text], then ‖u‖p ≤ C‖ϕ‖p where the constant C is independent of ϕ. In particular, we prove L1 estimates and obtain Lp estimates by interpolation.