Extension with growth estimates of holomorphic functions defined on singular analytic spaces

TL;DR

This paper establishes conditions for extending holomorphic functions from singular analytic subsets within convex domains to the entire domain, providing growth estimates using integral formulas and residual currents.

Contribution

It introduces new criteria and methods for holomorphic extension on singular spaces with growth control, utilizing residual currents and integral representations.

Findings

Extension conditions for holomorphic functions on singular spaces

Growth estimates in BMO and L^q spaces

Use of residual currents and integral formulas for extension

Abstract

Let D be a strictly convex domain and X be a singular analytic subset of C^2 such that the intersection of X and D is non empty. We give conditions under which a function holomophic on the intersection of X and D can be extended holomorphically to D with growth estimates of BMO or L^q type. The extension is given by mean of integral representation formulas and new residual currents.