Multilinear interpolation between adjoint operators

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dc.creatorGrafakos, Loukas
dc.creatorTao, Terence
dc.date2001-11-12
dc.date.accessioned2026-07-07T04:44:33Z
dc.date.available2026-07-07T04:44:33Z
dc.descriptionMultilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak $L^q$ estimate for a single index $q$ (which may be less than one) and that all the adjoints of the multilinear operator are of similar nature, and thus they also satisfy the same weak $L^q$ estimate. Under this assumption, in this expository note we give a general multilinear interpolation theorem which allows one to obtain strong type boundedness for the operator (and all of its adjoints) for a large set of exponents. The key point in the applications we discuss is that the interpolation theorem can handle the case $q \leq 1$. When $q > 1$, weak $L^q$ has a predual, and such strong type boundedness can be easily obtained by duality and multilinear interpolation.
dc.description6 pages, no figures, submitted, J. Funct. Anal
dc.identifierhttps://arxiv.org/abs/math/0111141
dc.identifierhttp://arxiv.org/abs/math/0111141
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62632
dc.subjectFunctional Analysis
dc.subjectClassical Analysis and ODEs
dc.subjectPrimary 46B70. Secondary 46E30, 42B99
dc.titleMultilinear interpolation between adjoint operators
dc.typetext

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