L^p-APPROXIMATION OF HOLOMORPHIC FUNCTIONS ON A CLASS OF CONVEX DOMAINS. Issue 3 (23rd April 2018) - HA, LY KIM
Abstract : Let [STIX]x1D6FA be a member of a certain class of convex ellipsoids of finite/infinite type in C^2 . In this paper, we prove that every holomorphic function in L^p([STIX]x1D6FA) can be approximated by holomorphic functions on [STIX]x1D6FA in L^p([STIX]x1D6FA) -norm, for 1≤ p<∞ . For the case p=∞, the continuity up to the boundary is additionally required. The proof is based on L^p bounds in the additive Cousin problem.