Displaying similar documents to “Uniform bounds for the bilinear Hilbert transforms (II).”

A uniform estimate for quartile operators.

Christoph Thiele (2002)

Revista Matemática Iberoamericana

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There is a one parameter family of bilinear Hilbert transforms. Recently, some progress has been made to prove Lp estimates for these operators uniformly in the parameter. In the current article we present some of these techniques in a simplified model...

Corrigenda: .

Alexander Nagel, Elias M. Stein (2005)

Revista Matemática Iberoamericana

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We wish to acknowledge and correct an error in a proof in our paper , which appeared in Revista Matemática Iberoamericana, volume 20, number 2, 2004, pages 531-561.

Corrigendum to .

Themis Mitsis (2005)

Revista Matemática Iberoamericana

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In the paper , appeared in Rev. Mat. Iberoamericana 20 (2004), 381-393, the author claimed that an (n,2)-set must have full Hausdorff dimension. However, as pointed out by Terence Tao and John Bueti, the proof contains an error.

Multi-parameter paraproducts.

Camil Muscalu, Jill Pipher, Terence Tao, Christoph Thiele (2006)

Revista Matemática Iberoamericana

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We prove that classical Coifman-Meyer theorem holds on any polidisc T or arbitrary dimension d ≥ 1.

Solution to the gradient problem of C.E. Weil.

Zoltán Buczolich (2005)

Revista Matemática Iberoamericana

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In this paper we give a complete answer to the famous gradient problem of C. E. Weil. On an open set G ⊂ R we construct a differentiable function f: G → R for which there exists an open set Ω ⊂ R such that ∇f(p) ∈ Ω for a p ∈ G but ∇f(q) ∉ Ω for almost every q ∈ G. This shows that the Denjoy-Clarkson property does not hold in higher dimensions.

Time-frequency analysis of Sjöstrand's class.

Karlheinz Gröchenig (2006)

Revista Matemática Iberoamericana

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We investigate the properties an exotic symbol class of pseudodifferential operators, Sjöstrand's class, with methods of time-frequency analysis (phase space analysis). Compared to the classical treatment, the time-frequency approach leads to striklingly simple proofs of Sjöstrand's fundamental results and to far-reaching generalizations.

A generalized sharp Whitney theorem for jets.

Charles Fefferman (2005)

Revista Matemática Iberoamericana

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Suppose that, for each point x in a given subset E ⊂ R, we are given an m-jet f(x) and a convex, symmetric set σ(x) of m-jets at x. We ask whether there exist a function F ∈ C(R) and a finite constant M, such that the m-jet of F at x belongs to f(x) + Mσ(x) for all x ∈ E. We give a necessary and sufficient condition for the existence of such F, M, provided each σ(x) satisfies a condition that we call "Whitnet w-convexity".

Extreme cases of weak type interpolation.

Evgeniy Pustylnik (2005)

Revista Matemática Iberoamericana

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We consider quasilinear operators T of joint weak type (a, b; p, q) (in the sense of [2]) and study their properties on spaces Lφ,E with the norm ||φ(t) f*(t)||Ê, where Ê is arbitrary rearrangement-invariant space with respect to the measure dt/t. A space Lφ,E is said to be "close" to one of the endpoints of interpolation if the corresponding Boyd index of this space is equal to 1/a or...