Vol. 110, No. 1, 1984

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ISSN: 0030-8730
An interpolation theorem for analytic families of operators acting on certain Hp spaces

Eugenio Hernandez

Vol. 110 (1984), No. 1, 113–118
Abstract

The main objective of this paper is to obtain an interpolation theorem for families of operators acting on atomic Hp spaces, 0 < p 1. We prove that if 0 < p0 < p1 1 and {Tz}, z S = {z C0 Real z 1}, is an analytic and admissible family of linear transformations such that Tj+iy maps Hpj into Lpj, where −∞ < y < , with norm not exceeding Aj, j = 0,1, then for all 𝜃, 0 𝜃 1, T𝜃 maps Hr into Lr with norm not exceeding cA01𝜃A1𝜃, where 1∕r = (1 𝜃)∕p0 + 𝜃∕p1.

Mathematical Subject Classification 2000
Primary: 47B38
Secondary: 46E35, 46M35
Milestones
Received: 8 March 1982
Revised: 16 December 1982
Published: 1 January 1984
Authors
Eugenio Hernandez