On the Hardy space H¹ on products of half-spaces

Nativi Viana Pereira Bertolo

Vol. 138 (1989), No. 2, 347–356

DOI: 10.2140/pjm.1989.138.347

Abstract

We show that the Hardy space H_anal¹(R₊² × R₊²) can be identified with the class of functions f such that f and all its double and partial Hilbert transforms H_kf belong to L¹(R²). A basic tool used in the proof is the bisubharmonicity of |F|^q, where F is a vector field that satisfies a generalized conjugate system of Cauchy-Riemann type.

Mathematical Subject Classification 2000

Primary: 46E15

Secondary: 32A35, 42B30

Milestones

Received: 30 December 1987

Published: 1 June 1989