Displaying similar documents to “Recent progress on the Kakeya conjecture.”

An X-ray transform estimate in R.

Izabella Laba, Terence Tao (2001)

Revista Matemática Iberoamericana

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We prove an x-ray estimate in general dimension which is a stronger version of Wolff's Kakeya estimate [12]. This generalizes the estimate in [13], which dealt with the n = 3 case.

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.

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|...

Heisenberg Hausdorff Dimension of Besicovitch Sets

Laura Venieri (2014)

Analysis and Geometry in Metric Spaces

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We consider (bounded) Besicovitch sets in the Heisenberg group and prove that Lp estimates for the Kakeya maximal function imply lower bounds for their Heisenberg Hausdorff dimension.

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...