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 $${A_p(\mathbb{C})}$$ and $${A^0_p(\mathbb{C})}$$ 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 $${q \leq p}$$ and investigate when the range of the restriction map on $${A_p(\mathbb{C})}$$ or $${A^0_p(\mathbb{C})}$$ contains certain subspaces associated in a natural way with the smaller weight q.