Composition operators on Musielak-Orlicz spaces of Bochner type
The invertible, closed range, compact, Fredholm and isometric composition operators on Musielak-Orlicz spaces of Bochner type are characterized in the paper.
Composition operators on the Bergman space
Composition operators on the Dirichlet space and related problems.
Composition operators on vector-valued Hardy spaces.
Composition operators on W 1 X are necessarily induced by quasiconformal mappings
Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to L q(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W 1 X to W 1 X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.
Computing norms and critical exponents of some operators in -spaces
Concentration of measure and logarithmic Sobolev inequalities
Concentration-Compactness Principle for embedding into multiple exponential spaces on unbounded domains
Let be a domain and let . We prove the Concentration-Compactness Principle for the embedding of the space into an Orlicz space corresponding to a Young function which behaves like for large . We also give the result for the embedding into multiple exponential spaces. Our main result is Theorem where we show that if one passes to unbounded domains, then, after the usual modification of the integrand in the Moser functional, the statement of the Concentration-Compactnes Principle is very...
Concerning holomorphy types for Banach spaces
Concerning the Banach-Stone theorem
Conditions de bornitude et espaces de fonctions mesurables
Conditions implying regularity of the three dimensional Navier-Stokes equation
We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac-like inequalities. As part of our methods, we give a different approach to a priori estimates of Foiaş, Guillopé and Temam.
Configuration space properties of the S-matrix and time delay in potential scattering
Constantes de Grothendieck et fonctions de type positif sur les sphères
Constructing a relativistic heat flow by transport time steps
Construction of an orthonormal basis in and
Construction of Dilations of Positive Lp-Contractions.
Construction of Sobolev spaces of fractional order with sub-riemannian vector fields
Given a smooth family of vector fields satisfying Chow-Hörmander’s condition of step 2 and a regularity assumption, we prove that the Sobolev spaces of fractional order constructed by the standard functional analysis can actually be “computed” with a simple formula involving the sub-riemannian distance.Our approach relies on a microlocal analysis of translation operators in an anisotropic context. It also involves classical estimates of the heat-kernel associated to the sub-elliptic Laplacian.
Continuité sur les espaces de Besov des opérateurs définis par des intégrales singulières
On donne un critère très simple de continuité des opérateurs définis par des intégrales singulières sur les espaces de Besov homogènes pour . Quelques exemples, utilisant notamment l’opérateur de paraproduit, illustrent ensuite l’emploi de ce critère.
Continuité sur les espaces de Hölder et de Sobolev des opérateurs définis par des intégrales singulières