Displaying similar documents to “An X-ray transform estimate in Rn.”

Recent progress on the Kakeya conjecture.

Nets Katz, Terence Tao (2002)

Publicacions Matemàtiques

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We survey recent developments on the Kakeya problem. [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].

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. ...

The FBI transform, operators with nonsmooth coefficients and the nonlinear wave equation

Daniel Tataru (1999)

Journées équations aux dérivées partielles

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The aim of this work is threefold. First we set up a calculus for partial differential operators with nonsmooth coefficients which is based on the FBI (Fourier-Bros-Iagolnitzer) transform. Then, using this calculus, we prove a weaker version of the Strichartz estimates for second order hyperbolic equations with nonsmooth coefficients. Finally, we apply these new Strichartz estimates to second order nonlinear hyperbolic equations and improve the local theory, i.e. prove local well-posedness...

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...

Semigroup commutators under differences (II).

Nicholas Th. Varopoulos (1993)

Revista Matemática Iberoamericana

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This is the second instalment of my previous paper with the same title, [1]. This paper consists of two different parts. The first part is devoted to improvements of the results developed in [1]. These improvements are described in section 0.1 below and developed in sections 1 to 5, and 9 to 10; they are in fact technically distinct from [1] and rely on a systematic use of microlocalisation in the context of Hörmander-Weyl calculus. These paragraphs can therefore be read quite independently...

An improved bound for Kakeya type maximal functions.

Thomas Wolff (1995)

Revista Matemática Iberoamericana

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The purpose of this paper is to improve the known results (specifically [1]) concerning L boundedness of maximal functions formed using 1 x δ x ... x δ tubes.

On the two weights problem for the Hilbert transform.

Nets Hawk Katz, Cristina Pereyra (1997)

Revista Matemática Iberoamericana

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In this paper, we prove sufficient conditions on pairs of weights (u,v) (scalar, matrix or operator valued) so that the Hilbert transform H f(x) = p.v. ∫ [f(y) / x - y] dy, is bounded from L2(u) to L2(v).

Unique continuation for |Δu| ≤ V |∇u| and related problems.

Thomas H. Wolff (1990)

Revista Matemática Iberoamericana

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Much of this paper will be concerned with the proof of the following Theorem 1. Suppose d ≥ 3, r = max {d, (3d - 4)/2}. If V ∈ Lloc r(Rd), then the differential inequality |Δu| ≤ V |∇u| has the strong unique continuation property in the following sense: If u belongs to the Sobolev space Wloc 2,p and if |Δu|...