Pseudoconvex classes of functions. I. Pseudoconcave and pseudoconvex sets

Zbigniew Slodkowski

Vol. 134 (1988), No. 2, 343–376

DOI: 10.2140/pjm.1988.134.343

Abstract

An axiomatic definition of a pseudoconvex class of functions is developed. The models include classes of subharmonic, plurisubharmonic, q-plurisubharmonic, convex and q-convex functions, and many others. Notions of dual class of functions and of pseudoconcave and pseudoconvex sets are introduced and studied. The results have applications to complex interpolation of normed spaces, given elsewhere.

Mathematical Subject Classification 2000

Primary: 32F05

Secondary: 31C05, 31C10, 32F10

Milestones

Received: 7 April 1987

Revised: 11 September 1987

Published: 1 October 1988