On isometries of Hardy spaces on compact abelian groups

Jun-ichi Tanaka

Vol. 95 (1981), No. 1, 219–232

DOI: 10.2140/pjm.1981.95.219

Abstract

Let H^p(m), 0 < p ≦∞, be the Hardy spaces on a quotient K of the Bohr group. In this paper we completely determine the isometries of H^p(m), p≠2, onto itself. Our result is a generalization of a recent work of Muhly who determined the isometries of H^p(m) onto itself under the assumption that the dual group of K is countable, and it may be regarded as a partial answer to a question posed by Muhly.

Mathematical Subject Classification 2000

Primary: 43A17

Secondary: 46J15

Milestones

Received: 24 October 1979

Published: 1 July 1981