Lp‐Estimates for the ∂¯b‐equation on a class of infinite type domains

Abstract

AbstractWe prove estimates, , for solutions to the tangential Cauchy–Riemann equations on a class of infinite type domains . The domains under consideration are a class of convex ellipsoids, and we show that if is a ‐closed (0,1)‐form with coefficients in , then there exists an explicit solution u satisfying . Moreover, when , we show that there is a gain in regularity to an f‐Hölder space.We also present two applications. The first is a solution to the ‐equation, that is, given a smooth (0,1)‐form ϕ on with an L1‐boundary value, we can solve the Cauchy–Riemann equation so that where C is independent of and ϕ. The second application is a discussion of the zero sets of holomorphic functions with zero sets of functions in the Nevanlinna class within our class of domains.