On the Equivalence of Holomorphic and Plurisubharmonic Phragmen-Lindeloef Principles

摘要

There are several papers in recent years which studied partial differential operators P(D) on classes of infinitely differentiable functions on convex open sets in R~N or C~N in terms of Phragmen-Lindeloef type estimates for pluri-subharmonic functions on algebraic varieties. In the early work of Hoer-mander it is shown that the surjectivity of P(D) on the space of all real analytic functions on a convex open set in R~N is equivalent to Phragmen-Lindeloef conditions on the tangent cone at infinity of the variety V(P):= {z∈C~N∣P(z) = 0}.