The Range of the Restriction Map for a Multiplicity Variety in Hörmander Algebras of Entire Functions

Abstract

Characterizations of interpolating multiplicity varieties for Hörmander algebras Ap(ℂ) and A0p(ℂ) of entire functions were obtained by Berenstein and Li (J Geom Anal 5(1):1-48, 1995) and Berenstein et al. (Can J Math 47(1):28-43, 1995) for a radial subharmonic weight p with the doubling property. In this note we consider the case when the multiplicity variety is not interpolating, we compare the range of the associated restriction map for two weights q ≤ p and investigate when the range of the restriction map on Ap(ℂ) or A0p(ℂ) contains certain subspaces associated in a natural way with the smaller weight q. © 2013 Springer Basel.