Classical Solutions of Nonlinear Schrödinger Equations in Higher Dimensions.
Coarea integration in metric spaces
Let be a metric space with a doubling measure, be a boundedly compact metric space and be a Lebesgue precise mapping whose upper gradient belongs to the Lorentz space , . Let be a set of measure zero. Then for -a.e. , where is the -dimensional Hausdorff measure and is the -codimensional Hausdorff measure. This property is closely related to the coarea formula and implies a version of the Eilenberg inequality. The result relies on estimates of Hausdorff content of level sets...
Coercive inequalities on weighted Sobolev spaces
Coercivité de formes sesquilinéaires intégro-différentielles dans des espaces de Sobolev avec poids
Compacité par compensation
Compacité par compensation : condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant
Compacité par compensation et espaces de Hardy
Compact and continuous embeddings of logarithmic Bessel potential spaces
We establish compact and continuous embeddings for Bessel potential spaces modelled upon generalized Lorentz-Zygmund spaces. The target spaces are either of Lorentz-Zygmund or Hölder type.
Compact embedding of a degenerate Sobolev space and existence of entire solutions to a semilinear equation for a Grushin-type operator
Compact embedding theorems for generalized Sobolev spaces
In this Note we give some compact embedding theorems for Sobolev spaces, related to -tuples of vectors fields of class on .
Compact Embeddings for Weighted Orlicz-Sobolev Spaces on IRN.
Compact embeddings of Besov spaces involving only slowly varying smoothness
We characterize compact embeddings of Besov spaces involving the zero classical smoothness and a slowly varying smoothness into Lorentz-Karamata spaces , where is a bounded domain in and is another slowly varying function.
Compact embeddings of Brézis-Wainger type.
Let Ω be a bounded domain in Rn and denote by idΩ the restriction operator from the Besov space Bpq1+n/p(Rn) into the generalized Lipschitz space Lip(1,-α)(Ω). We study the sequence of entropy numbers of this operator and prove that, up to logarithmic factors, it behaves asymptotically like ek(idΩ) ~ k-1/p if α > max (1 + 2/p + 1/q, 1/p). Our estimates improve previous results by Edmunds and Haroske.
Compact imbedding of weighted Sobolev space defined on an unbounded domain. I.
Compact imbedding of weighted Sobolev space defined on an unbounded domain. II.
Compact imbeddings in weighted Sobolev spaces and nonlinear boundary value problems
Compact operators and approximation spaces
We investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.
Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators
A small perturbation method is developed and employed to construct frames with compactly supported elements of small shrinking support for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure space in the presence of a nonnegative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows one, in particular, to construct compactly supported frames for Besov and Triebel-Lizorkin spaces on the sphere, on the interval with...
Compactly Supported Refinable Distributions in Triebel-Lizorkin Spaces and Besov Spaces.
Compactness criteria in function spaces
The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves more explicitly the symmetry between time and frequency than the classical conditions. The result is first stated and proved for , and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin, modulation and Bargmann-Fock spaces.