Comportement asymptotique des valeurs propres d'opérateurs elliptiques dégénérés
We characterize stability under composition of ultradifferentiable classes defined by weight sequences M, by weight functions ω, and, more generally, by weight matrices , and investigate continuity of composition (g,f) ↦ f ∘ g. In addition, we represent the Beurling space and the Roumieu space as intersection and union of spaces and for associated weight sequences, respectively.
The Banach operator ideal of (q,2)-summing operators plays a fundamental role within the theory of s-number and eigenvalue distribution of Riesz operators in Banach spaces. A key result in this context is a composition formula for such operators due to H. König, J. R. Retherford and N. Tomczak-Jaegermann. Based on abstract interpolation theory, we prove a variant of this result for (E,2)-summing operators, E a symmetric Banach sequence space.
We establish a composition calculus for Fourier integral operators associated with a class of smooth canonical relations . These canonical relations, which arise naturally in integral geometry, are such that : is a Whitney fold and : is a blow-down mapping. If , , then a class of pseudodifferential operators with singular symbols. From this follows boundedness of with a loss of 1/4 derivative.
The Hilbert matrix acts on Hardy spaces by multiplication with Taylor coefficients. We find an upper bound for the norm of the induced operator.
We characterize the boundedness and compactness of composition operators from weighted Bergman-Privalov spaces to Zygmund type spaces on the unit disk.