Interpolationsfunktoren, Folgenideale und Operatorenideale
Intrinsic atomic characterizations of function spaces on domains.
Intrinsic characterizations of distribution spaces on domains
We give characterizations of Besov and Triebel-Lizorkin spaces and in smooth domains via convolutions with compactly supported smooth kernels satisfying some moment conditions. The results for s ∈ ℝ, 0 < p,q ≤ ∞ are stated in terms of the mixed norm of a certain maximal function of a distribution. For s ∈ ℝ, 1 ≤ p ≤ ∞, 0 < q ≤ ∞ characterizations without use of maximal functions are also obtained.
Invariance par difféomorphisme d'espace de Sobolev. Espace de Sobolev d'une variété. Applications
Isomorphic type of the space of smooth functions determined by a finite family of differential operators.
Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces
In Hörmander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions. We prove that the operators corresponding to these problems are isomorphisms between appropriate Hörmander spaces. The regularity of the functions which form these spaces is characterized by a pair of number parameters and a function parameter varying regularly at infinity in the sense...
Isoperimetry, Logarithmic Sobolev Inequalities on the Discrete Cube, and Margulies' Graph Connectivity Theorem.