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Weak type $(1,1)$ bounds for rough operators

Michael Christ
- 01 Jul 1988 - 
- Vol. 128, Iss: 1, pp 19
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This article is published in Annals of Mathematics.The article was published on 1988-07-01. It has received 224 citations till now.

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Plancherel Type Estimates and Sharp Spectral Multipliers

Xuan Thinh Duong, +2 more
- 20 Dec 2002 - 
TL;DR: In this paper, the sharp Hormander-type spectral multiplier theorems for self-adjoint positive definite operators on L 2(X,μ), where X is any open subset of a space of homogeneous type, were studied.
Journal ArticleDOI

Strong variational and jump inequalities in harmonic analysis

Roger L. Jones, +2 more
- 24 Jul 2008 - 
TL;DR: In this paper, the authors prove variational and jump inequalities for a large class of linear operators arising in harmonic analysis, and prove jump inequalities also for a class of operators arising from harmonic analysis.
Journal ArticleDOI

The Bochner-Riesz conjecture implies the restriction conjecture

Terence Tao
- 01 Feb 1999 - 
Journal ArticleDOI

Weighted norm inequalities for homogeneous singular integrals

Javier Duoandikoetxea
- 01 Feb 1993 - 
TL;DR: In this article, the authors proved weighted norm inequalities for homogeneous singular integrals when only a size condition is assumed on the restriction of the kernel to the unit sphere, and the same results hold for the operator obtained by modifying the centered Hardy-Littlewood maximal operator over balls with a degree zero homogeneous function.
Journal ArticleDOI

L p IMPROVING BOUNDS FOR AVERAGES ALONG CURVES

Terence Tao, +1 more
- 28 Jan 2003 - 
TL;DR: In this paper, the mapping properties of averaging operators on curves have been studied, where the exponents are sharp except for the endpoints of the average exponents, where they are smooth except for endpoints.