Volume 3,  Issue 2, 2002

Article 19

LITTLEWOOD'S INEQUALITY FOR p-BIMEASURES

NASSER M. TOWGHI

RAYTHEON SYSTEM COMPANY
528 BOSTON POST ROAD
MAIL STOP 2-142,
SUDBURY, MA 01776
E-Mail: Nasser_M_Towghi@res.raytheon.com

Received 10 April, 2001; Accepted 16 November, 2001.
Communicated by: L. Losonczi

ABSTRACT.   In this paper we extend an inequality of Littlewood concerning the higher variations of functions of bounded Fréchet variations of two variables (bimeasures) to a class of functions that are p-bimeasures, by using the machinery of vector measures. Using random estimates of Kahane-Salem-Zygmund, we show that the inequality is sharp.
Key words:
Inequalities, Bimeasures, Fréchet variation, p-variations, Bounded variations.

2000 Mathematics Subject Classification:
26B15, 26A42, 28A35, 28A25.

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