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Modulation invariant and multilinear singular integral operators

Michael Christ (2005/2006)

Séminaire Bourbaki

In a series of papers beginning in the late 1990s, Michael Lacey and Christoph Thiele have resolved a longstanding conjecture of Calderón regarding certain very singular integral operators, given a transparent proof of Carleson’s theorem on the almost everywhere convergence of Fourier series, and initiated a slew of further developments. The hallmarks of these problems are multilinearity as opposed to mere linearity, and especially modulation symmetry. By modulation is meant multiplication by characters...

Modulation space estimates for multilinear pseudodifferential operators

Árpád Bényi, Kasso A. Okoudjou (2006)

Studia Mathematica

We prove that for symbols in the modulation spaces p , q , p ≥ q, the associated multilinear pseudodifferential operators are bounded on products of appropriate modulation spaces. In particular, the symbols we study here are defined without any reference to smoothness, but rather in terms of their time-frequency behavior.

Moltiplicatori spettrali per l'operatore di Ornstein-Uhlenbeck

Giancarlo Mauceri (2004)

Bollettino dell'Unione Matematica Italiana

Questa è una rassegna di alcuni risultati recenti sui moltiplicatori spettrali dell'operatore di Ornstein-Uhlenbeck, un laplaciano naturale sullo spazio euclideo munito della misura gaussiana. I risultati sono inquadrati nell'ambito della teoria generale dei moltiplicatori spettrali per laplaciani generalizzati.

Moment sequences and abstract Cauchy problems

Claus Müller (2003)

Commentationes Mathematicae Universitatis Carolinae

We give a new characterization of the solvability of an abstract Cauchy problems in terms of moment sequences, using the resolvent operator at only one point.

Monotone operators. A survey directed to applications to differential equations

Jan Franců (1990)

Aplikace matematiky

The paper deals with the existence of solutions of the form A u = b with operators monotone in a broader sense, including pseudomonotone operators and operators satisfying conditions S and M . The first part of the paper which has a methodical character is concluded by the proof of an existence theorem for the equation on a reflexive separable Banach space with a bounded demicontinuous coercive operator satisfying condition ( M ) 0 . The second part which has a character of a survey compares various types of...

Monotone operators in divergence form with x -dependent multivalued graphs

Gilles Francfort, François Murat, Luc Tartar (2004)

Bollettino dell'Unione Matematica Italiana

We prove the existence of solutions to - div a x , grad u = f , together with appropriate boundary conditions, whenever a x , e is a maximal monotone graph in e , for every fixed x . We propose an adequate setting for this problem, in particular as far as measurability is concerned. It consists in looking at the graph after a 45 rotation, for every fixed x ; in other words, the graph d a x , e is defined through d - e = φ x , d + e , where φ is a Carathéodory contraction in R N . This definition is shown to be equivalent to the fact that a ( x , ) is pointwise monotone...

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