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Multilinear Calderón Zygmund theory
 ADV. IN MATH. 40
, 1996
"... A systematic treatment of multilinear CalderónZygmundoperators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, the multilinear T1 theorem, anda variety of results regarding multilinear multiplier operators. ..."
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Cited by 93 (19 self)
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A systematic treatment of multilinear CalderónZygmundoperators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, the multilinear T1 theorem, anda variety of results regarding multilinear multiplier operators.
Weighted inequalities for multilinear fractional integral operators
 Collect. Math
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On multilinear singular integrals of CalderónZygmund type
, 2011
"... A variety of results regarding multilinear CalderónZygmund singular integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discret ..."
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Cited by 19 (4 self)
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A variety of results regarding multilinear CalderónZygmund singular integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur’s test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators. A maximal operator associated with multilinear singular integrals is also introduced and employed to obtain weighted norm inequalities.
Multilinear interpolation between adjoint operators
, 2003
"... Abstract. Multilinear interpolation is a powerful tool used in obtainingstrong type boundedness for a variety of operators assumingonly a finite set of restricted weaktype estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak L q estimate for a single ind ..."
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Cited by 17 (9 self)
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Abstract. Multilinear interpolation is a powerful tool used in obtainingstrong type boundedness for a variety of operators assumingonly a finite set of restricted weaktype 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 strongtype 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 ≤ 1. When q>1, weak L q has a predual, and such strongtype boundedness can be easily obtained by duality and multilinear interpolation (c.f. [1], [5], [7], [12], [14]). 1. Multilinear operators We begin by setting up some notation for multilinear operators. Let m ≥ 1bean integer. We suppose that for 0 ≤ j ≤ m, (Xj,µj) are measure spaces endowed with
Transference on certain multilinear multiplier operators
 MR1808390 (2002c:42013
"... multilinear multiplier operators ..."
THE MULTILINEAR STRONG MAXIMAL FUNCTION
"... Abstract. A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the boundedness of this multivariable operator on products of ..."
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Abstract. A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the boundedness of this multivariable operator on products of weighted Lebesgue spaces equipped with multiple weights are obtained. Results for other multi(sub)linear maximal functions associated with bases of open sets are studied too. Bilinear interpolation results between distributional estimates, such as those satisfied by the multivariable strong maximal function, are also proved. 1.
The Hörmander multiplier theorem for multilinear operators
 J. Reine Angew. Math. (2012
"... Abstract. In this paper, we provide a version of the MihlinHörmander multiplier theorem for multilinear operators in the case where the target space is L p for p ≤ 1. This extends a recent result of Tomita [15] who proved an analogous result for p> 1. 1. ..."
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Cited by 10 (5 self)
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Abstract. In this paper, we provide a version of the MihlinHörmander multiplier theorem for multilinear operators in the case where the target space is L p for p ≤ 1. This extends a recent result of Tomita [15] who proved an analogous result for p> 1. 1.