Singular integrals on product H spaces.
Robert Fefferman (1985)
Revista Matemática Iberoamericana
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Robert Fefferman (1985)
Revista Matemática Iberoamericana
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Josfina Alvarez, Jorge Hounie (1999)
Studia Mathematica
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We prove the continuity of an oscillatory singular integral operator T with polynomial phase P(x,y) on an atomic space related to the phase P. Moreover, we show that the cancellation condition to be imposed on T holds under more general conditions. To that purpose, we obtain a van der Corput type lemma with integrability at infinity.
A. Calderón, A. Zygmund (1979)
Studia Mathematica
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Loukas Grafakos, Rodolfo H. Torres (2002)
Publicacions Matemàtiques
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A variety of results regarding multilinear singular Calderón-Zygmund 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....
Margaret Murray (1987)
Studia Mathematica
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Jean-Lin Journé (1985)
Revista Matemática Iberoamericana
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Dashan Fan, Yibiao Pan (1997)
Publicacions Matemàtiques
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In this paper we study a singular integral operator T with rough kernel. This operator has singularity along sets of the form {x = Q(|y|)y'}, where Q(t) is a polynomial satisfying Q(0) = 0. We prove that T is a bounded operator in the space L2(Rn), n ≥ 2, and this bound is independent of the coefficients of Q(t). We also obtain certain Hardy type inequalities related to this operator.
Michel Frazier, Rodolfo Torres, Guido Weiss (1988)
Revista Matemática Iberoamericana
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Calderón-Zygmund operators are generalizations of the singular integral operators introduced by Calderón and Zygmund in the fifties [CZ]. These singular integrals are principal value convolutions of the form Tf(x) = límε→0 ∫|x-y|>ε K(x-y) f(y) dy = p.v.K * f(x), where f belongs to some class of test functions.
Steve Hofmann, John L. Lewis (2001)
Revista Matemática Iberoamericana
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We establish L and L bounds for a class of square functions which arises in the study of singular integrals and boundary value problems in non-smooth domains. As an application, we present a simplified treatment of a class of parabolic smoothing operators which includes the caloric single layer potential on the boundary of certain minimally smooth, non-cylindrical domains.
Lung-Kee Chen (1987)
Studia Mathematica
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