Composition operator on Bergman-Orlicz space.
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 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-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...
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.
(Conférence n°3) Applications radonifiantes dans l'espace des séries convergentes
Configuration space properties of the S-matrix and time delay in potential scattering
Constructing a relativistic heat flow by transport time steps
Construction of Dilations of Positive Lp-Contractions.
Continuity of Pseudo-differential Operators on Bessel And Besov Spaces
We study the continuity of pseudo-differential operators on Bessel potential spaces Hs|p (Rn ), and on the corresponding Besov spaces B^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function.
Continuity of superposition operators on and
Continuous and compact imbeddings of weighted Sobolev spaces. I
Continuous selections for a class of non-convex multivalued maps
Contre-exemples associés aux théorèmes de Rosenthal. Quelques propriétés liées à ces résultats
Convergence of greedy approximation II. The trigonometric system
We study the following nonlinear method of approximation by trigonometric polynomials. For a periodic function f we take as an approximant a trigonometric polynomial of the form , where is a set of cardinality m containing the indices of the m largest (in absolute value) Fourier coefficients f̂(k) of the function f. Note that Gₘ(f) gives the best m-term approximant in the L₂-norm, and therefore, for each f ∈ L₂, ||f-Gₘ(f)||₂ → 0 as m → ∞. It is known from previous results that in the case of...
Convergence of orthogonal series of projections in Banach spaces
For a sequence of mutually orthogonal projections in a Banach space, we discuss all possible limits of the sums in a “strong” sense. Those limits turn out to be some special idempotent operators (unbounded, in general). In the case of X = L₂(Ω,μ), an arbitrary unbounded closed and densely defined operator A in X may be the μ-almost sure limit of (i.e. μ-a.e. for all f ∈ (A)).
Convergence of Taylor series in Hardy and Besov spaces.
Convergences de séries dans les espaces d'Orlicz