Displaying similar documents to “Maximal functions and Hilbert transforms associated to polynomials.”

The work of José Luis Rubio de Francia (III).

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.

Multiple singular integrals and maximal functions along hypersurfaces

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 L p , 1 < p < ∞ . 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...

Multilinear singular integrals.

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. ...

Directional operators and mixed norms.

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...

Fourier analysis in several parameters.

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].

Variants of the Calderón-Zygmund theory for L-spaces.

Anthony Carbery (1986)

Revista Matemática Iberoamericana

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The purposes of this paper may be described as follows: (i) to provide a useful substitute for the Cotlar-Stein lemma for Lp-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions); (ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed? (iii) to simplify and extend the work of Duoandikoetxea...