Traces of a weighted Sobolev space in a singular case
Traces of anisotropic Besov-Lizorkin-Triebel spaces---a complete treatment of the borderline cases
Including the previously untreated borderline cases, the trace spaces (in the distributional sense) of the Besov-Lizorkin-Triebel spaces are determined for the anisotropic (or quasi-homogeneous) version of these classes. The ranges of the traces are in all cases shown to be approximation spaces, and these are shown to be different from the usual spaces precisely in the cases previously untreated. To analyse the new spaces, we carry over some real interpolation results as well as the refined Sobolev...
Traces of Besov spaces on fractal h-sets and dichotomy results
We study the existence of traces of Besov spaces on fractal h-sets Γ with a special focus on assumptions necessary for this existence; in other words, we present criteria for the non-existence of traces. In that sense our paper can be regarded as an extension of Bricchi (2004) and a continuation of Caetano (2013). Closely connected with the problem of existence of traces is the notion of dichotomy in function spaces: We can prove that-depending on the function space and the set Γ-there occurs an...
Traces of Besov spaces revisited.
Traces of functions of generalized Sobolev classes.
Traces of functions with a dominating mixed derivative in
We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in , with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to . The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.
Traces of Sobolev functions on the Ahlfors sets of Carnot groups.
Tractable embeddings of Besov spaces into Zygmund spaces
The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces. This can be expressed in terms of tractability envelopes.
Tractable embeddings of Besov spaces into Zygmund spaces, II
The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces.
Transference theory onHardy and Sobolev spaces
We show that the transference method of Coifman and Weiss can be extended to Hardy and Sobolev spaces. As an application we obtain the de Leeuw restriction theorems for multipliers.
Translation invariant projections in Sobolev spaces on tori in the L¹ and uniform norms
The idempotent multipliers on Sobolev spaces on the torus in the L¹ and uniform norms are characterized in terms of the coset ring of the dual group of the torus. This result is deduced from a more general theorem concerning certain translation invariant subspaces of vector-valued function spaces on tori.
Triangulations of closed sets and bases in function spaces.
Triebel-Lizorkin spaces for Hermite expansions
This paper develops some Littlewood-Paley theory for Hermite expansions. The main result is that certain analogues of Triebel-Lizorkin spaces are well-defined in the context of Hermite expansions.
Triebel-Lizorkin spaces on spaces of homogeneous type
In [HS] the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type were introduced. In this paper, the Triebel-Lizorkin spaces on spaces of homogeneous type are generalized to the case where , and a new atomic decomposition for these spaces is obtained. As a consequence, we give the Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type which were introduced by the maximal function characterization in [MS2].
Triebel-Lizorkin spaces with non-doubling measures
Suppose that μ is a Radon measure on , which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function inequality...
Trudinger–Moser inequality on the whole plane with the exact growth condition
Trudinger-Moser inequality is a substitute to the (forbidden) critical Sobolev embedding, namely the case where the scaling corresponds to . It is well known that the original form of the inequality with the sharp exponent (proved by Moser) fails on the whole plane, but a few modied versions are available. We prove a precised version of the latter, giving necessary and sufficient conditions for the boundedness, as well as for the compactness, in terms of the growth and decay of the nonlinear function....
Two observations on a theorem by Coifman
Two-microlocal Besov spaces and wavelets
Two-weight Sobolev-Poincaré inequalities and Harnack inequality for a class of degenerate elliptic operators
In this Note we prove a two-weight Sobolev-Poincaré inequality for the function spaces associated with a Grushin type operator. Conditions on the weights are formulated in terms of a strong weight with respect to the metric associated with the operator. Roughly speaking, the strong condition provides relationships between line and solid integrals of the weight. Then, this result is applied in order to prove Harnack's inequality for positive weak solutions of some degenerate elliptic equations....
Über äquivalente Normen in Sobolevschen Räumen mit Belegungsfunktion