Vol. 43, No. 2, 1972

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Some Hp spaces which are uncomplemented in Lp

Samuel Ebenstein

Vol. 43 (1972), No. 2, 327–339

Let Tj denote the compact group which is the Cartesian product of j copies of the circle where j is a positive integer or ω. If 1 p let Lp(Tj) denote the space of complex valued measurable functions which are integrable with respect to Haar measure on Tj. If j is finite we shall write n instead of j. The subspaces Hp(Tn) of LP(Tn), i.e. the Hardy spaces of Tn, have many well-known properties. A family of subspaces Hp(Tω) of the Lp(Tω) is defined and they are shown to have many of the same properties as the Hp(Tn). However a major difference between Hp(Tω) and Hp(Tn) is observed. If 1 < p < then Hp(Tn) is complemented in Lp(Tn), but Hp(Tω) is uncomplemented in Lp(Tω) for 1 < p < unless

p = 2.

Mathematical Subject Classification 2000
Primary: 43A70
Secondary: 46J15
Received: 12 April 1971
Revised: 13 August 1971
Published: 1 November 1972
Samuel Ebenstein