On the theory of class p operators and generalizations

Abstract

Motivated by integral-free representations of solutions of complex second-order partial differential equations Lu = 0 obtained from class P Bergman integral operators, we introduce a new type of infinite series (“P-series”) and show that their theory is an analog of the usual Bergman theory in integral form, of the same generality and in certain applications of greater utility. A basic spinoff of this theory is a novel kind of criterion for L [d] class P