Integral representations and transforms of -functions. II.
Let denote the real-valued functions continuous on the extended real line and vanishing at . Let denote the functions that are left continuous, have a right limit at each point and vanish at . Define to be the space of tempered distributions that are the th distributional derivative of a unique function in . Similarly with from . A type of integral is defined on distributions in and . The multipliers are iterated integrals of functions of bounded variation. For each , the spaces...
Nous précisons, dans le contexte microlocal Sobolev, les résultats de propagations de singularités obtenus par N. Hanges dans le contexte microlocal pour les opérateurs pseudo-differentiels à symbole principal réel et dont la variété caractéristique est la réunion de deux hypersurfaces lisses d’intersection non involutive. Nous obtenons également un résultat de propagation dans un cas non linéaire. Nos démonstrations consistent essentiellement à étudier l’action des paramétrices constantes par...
A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space .
We continue an investigation started in a preceding paper. We discuss tha classical result of Carleson connecting Carleson measures with the ∂-equation in a slightly more abstract framework than usual. We also consider a more recent result of Peter Jones which shows the existence of a solution for the ∂-equation, which satisfies simultaneously a good L∞ estimate and a good L1 estimate. This appears as a special case of our main result which can be stated as follows:Let (Ω, A, μ) be any measure space....