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Volume 3, Issue 2, Article 19 |
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Littlewood's Inequality for $p$-Bimeasures
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Authors: |
Nasser M. Towghi, |
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Keywords:
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Inequalities, Bimeasures, Fréchet variation, $p$-variations, Bounded variations. |
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Date Received:
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10/04/01 |
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Date Accepted:
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16/11/01 |
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Subject Codes: |
26B15,26A42,28A35,28A25.
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Editors: |
Laszlo Losonczi, |
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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.
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