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On multilinear singular integrals of Calderón-Zygmund type.

Loukas Grafakos, Rodolfo H. Torres (2002)

Publicacions Matemàtiques

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. A maximal...

On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations

A. I. Fedotov (2002)

Archivum Mathematicum

We prove the convergence of polynomial collocation method for periodic singular integral, pseudodifferential and the systems of pseudodifferential equations in Sobolev spaces H s via the equivalence between the collocation and modified Galerkin methods. The boundness of the Lagrange interpolation operator in this spaces when s > 1 / 2 allows to obtain the optimal error estimate for the approximate solution i.e. it has the same rate as the best approximation of the exact solution by the polynomials.

On the Fefferman-Phong inequality

Abdesslam Boulkhemair (2008)

Annales de l’institut Fourier

We show that the number of derivatives of a non negative 2-order symbol needed to establish the classical Fefferman-Phong inequality is bounded by n 2 + 4 + ϵ improving thus the bound 2 n + 4 + ϵ obtained recently by N. Lerner and Y. Morimoto. In the case of symbols of type S 0 , 0 0 , we show that this number is bounded by n + 4 + ϵ ; more precisely, for a non negative symbol a , the Fefferman-Phong inequality holds if ∂ x α ∂ ξ β a ( x , ξ ) are bounded for, roughly, 4 ≤ | α | + | β | ≤ n + 4 + ϵ . To obtain such results and others, we first prove an abstract result which says that...

Opérateurs pseudo-différentiels analytiques et opérateurs d'ordre infini

Louis Boutet de Monvel (1972)

Annales de l'institut Fourier

Cet article reprend et complète la partie qui concerne les opérateurs pseudo- différentiels analytiques dans un travail fait en collaboration avec P. Krée (Ann. Inst. Fourier, 17-1 (1967), 295-323). En particulier la théorie est généralisée aux opérateurs d’ordre infini.

Opérateurs pseudo-différentiels définis en un point

Ryuichi Ishimura (2006)

Annales Polonici Mathematici

We introduce the notion of pseudo-differential operators defined at a point and we establish a canonical one-to-one correspondence between such an operator and its symbol. We also prove the invertibility theorem for special type operators.

Oscillatory and Fourier integral operators with degenerate canonical relations.

Allan Greenleaf, Andreas Seeger (2002)

Publicacions Matemàtiques

We survey results concerning the L2 boundedness of oscillatory and Fourier integral operators and discuss applications. The article does not intend to give a broad overview; it mainly focuses on topics related to the work of the authors.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].

Currently displaying 81 – 100 of 148