Javier Duoandikoetxea (1991)
Publicacions Matemàtiques
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The aim of this paper is to review a set of articles ([6], [10], [11], [13], [16], [25]) of which José Luis Rubio de Francia was author and co-author written between 1985 and 1987.
Malabika Pramanik, Keith M. Rogers, Andreas Seeger (2011)
Studia Mathematica
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We prove a Calderón-Zygmund type estimate which can be applied to sharpen known regularity results on spherical means, Fourier integral operators, generalized Radon transforms and singular oscillatory integrals.
Wainger, Stephen (1998)
Documenta Mathematica
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Christoph M. Thiele (2002)
Publicacions Matemàtiques
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We survey the theory of multilinear singular integral operators with modulation symmetry. The basic example for this theory is the bilinear Hilbert transform and its multilinear variants. We outline a proof of boundedness of Carleson's operator which shows the close connection of this operator to multilinear singular integrals. We discuss particular multilinear singular integrals which historically arose in the study of eigenfunctions of Schrödinger operators. ...
J. Bourgain (1991)
Geometric and functional analysis
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Robert Fefferman (1986)
Revista Matemática Iberoamericana
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Clearly, one of the most basic contributions to the fields of real variables, partial differential equations and Fourier analysis in recent times has been the celebrated theorem of Calderón and Zygmund on the boundedness of singular integrals on R [1].
Antonio Córdoba Barba, José L. Rubio de Francia (1986)
Revista Matemática Iberoamericana
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Javier Duoandikoetxea (1986)
Annales de l'institut Fourier
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Maximal functions written as convolution with a multiparametric family of positive measures, and singular integrals whose kernel is decomposed as a multiple series of measures, are shown to be bounded in , . The proofs are based on the decomposition of the operators according to the size of the Fourier transform of the measures, assuming some regularity at zero and decay at infinity of these Fourier transforms. Applications are given to homogeneous singular integrals in product spaces...
Joe Howard (1970)
Colloquium Mathematicae
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Javier Duoandikoetxea (2002)
Publicacions Matemàtiques
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We present a survey of mixed norm inequalities for several directional operators, namely, directional Hardy-Littlewood maximal functions and Hilbert transforms (both appearing in the method of rotations of Calderón and Zygmund), X-ray transforms, and directional fractional operators related to Riesz type potentials with variable kernel. In dimensions higher than two several interesting questions remain unanswered. [Proceedings of the 6th International Conference...
Daniel M. Oberlin (1996)
Revista Matemática Iberoamericana
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Loukas Grafakos (2003)
Colloquium Mathematicae
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It is shown that maximal truncations of nonconvolution L²-bounded singular integral operators with kernels satisfying Hörmander’s condition are weak type (1,1) and -bounded for 1 < p< ∞. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar’s inequality. This inequality is not applicable here and the point of this article is to treat the boundedness of such maximal singular integral operators in an alternative way.