Displaying similar documents to “Modulation invariant and multilinear singular integral operators”

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. ...

On multilinear singular integrals of Calderón-Zygmund type.

Loukas Grafakos, Rodolfo H. Torres (2002)

Publicacions Matemàtiques

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A variety of results regarding multilinear singular Calderón-Zygmund integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur's test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators....

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].

Bilinear multipliers on Lorentz spaces

Francisco Villarroya (2008)

Czechoslovak Mathematical Journal

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We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.

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).

On oscillatory integral operators with folding canonical relations

Allan Greenleaf, Andreas Seeger (1999)

Studia Mathematica

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Sharp L p estimates are proven for oscillatory integrals with phase functions Φ(x,y), (x,y) ∈ X × Y, under the assumption that the canonical relation C Φ projects to T*X and T*Y with fold singularities.

Integral representations of unbounded operators by infinitely smooth kernels

Igor Novitskiî (2005)

Open Mathematics

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In this paper, we prove that every unbounded linear operator satisfying the Korotkov-Weidmann characterization is unitarily equivalent to an integral operator in L 2(R), with a bounded and infinitely smooth Carleman kernel. The established unitary equivalence is implemented by explicitly definable unitary operators.

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.