Distributional estimates for multilinear operators

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Distributional estimates for multilinear operators

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/4139

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Title: Distributional estimates for multilinear operators
Author: Bilyk, Dmytro, 1979-
Date: 2005
Publisher: University of Missouri--Columbia
Abstract: We prove that if a multilinear operator and all its adjoints map L1 x x L1 to L1/m,oo, then the distribution function of the operator applied to characteristic functions of sets of finite measure has exponential decay at infinity. These estimates are based only on the boundedness properties and not the specific structure of the operator. The result applies to multilinear Calderon-Zygmund operators and several maximal operators. We have also obtained similar distributional estimates for the bilinear Hilbert transform: . . . . . . . .These estimates refect the exponential decay of the distribution function at infinity and also, up to a logarithmic factor, cover the endpoint cases of the region treated by Lacey and Thiele. Distributional estimates of this type also imply the boundedness of the operator on other rearrangement invariant spaces, in particular, the local exponential integrability.
URI: http://hdl.handle.net/10355/4139
Other Identifiers: BilykD-050905-D1481

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