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Lp estimates for degenerate elliptic equations.

Antonio Sánchez-Calle (1988)

Revista Matemática Iberoamericana

In this note we are going to address the question of when a second order differential operator is controlled by a subelliptic second order differential operator.

Matrix triangulation of hypoelliptic boundary value problems

R. A. Artino, J. Barros-Neto (1992)

Annales de l'institut Fourier

Given a hypoelliptic boundary value problem on ω × [ 0 , T ) with ω an open set in R n , ( n > 1 ) , we show by matrix triangulation how to reduce it to two uncoupled first order systems, and how to estimate the eigenvalues of the corresponding matrices. Parametrices for the first order systems are constructed. We then characterize hypoellipticity up to the boundary in terms of the Calderon operator corresponding to the boundary value problem.

Microdistributions de Fourier classiques dans le cadre analytique réel

André Piriou (1984)

Annales de l'institut Fourier

On étudie une classe de microdistributions intégrales de Fourier représentées à l’aide de phases homogènes analytiques réelles, d’amplitudes qui sont des réalisations holomorphes tronquées de symboles analytiques classiques, et de contours d’intégration le long desquels la partie imaginaire de la phase a une propriété convenable de positivité. On donne des théorèmes de changement de phase et de composition transverse analogues à ceux du cas C ∞ , et on montre comment le calcul symbolique standard des...

Microlocal regularity at the boundary for pseudo-differential operators with the transmission property (I)

Maurice De Gosson (1982)

Annales de l'institut Fourier

This work is devoted to a systematic study of the microlocal regularity properties of pseudo-differential operators with the transmission property. We introduce a “boundary singular spectrum”, denoted ∂ W F ω ( u ) for distributions u ∈ D ' ( R + n ) , regular in the normal variable x n (thus, ∂ W F ω ( u ) = ∅ means that u ∈ ∩ s + t = 1 / 2 H s + t near the boundary), and it is shown that ∂ W F ω - m [ P ( u 0 ) x n > 0 ] is a subset of ∂ W F ( u ) if P has degree m and the transmission property. We finally prove that these results can bef used to examinate the (microlocal) regularity of the solutions of differential...

Modulation space estimates for multilinear pseudodifferential operators

Árpád Bényi, Kasso A. Okoudjou (2006)

Studia Mathematica

We prove that for symbols in the modulation spaces ℳ 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.

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