Pointwise multiplication in Triebel-Lizorkin spaces.
Necessary conditions on composition operators acting on Sobolev spaces of fractional order. The critical case 1 ... s ... n/p.
Spline Representations of Functions in Besov-Triebel-Lizorkin Spaces on Rn.
Superposition of functions in Sobolev spaces of fractional order. A survey
Approximation from sparse grids and function spaces of dominating mixed smoothness
We investigate the convergence and the rate of convergence in , 1 < p < ∞, of a bivariate interpolating (with respect to a sparse grid) trigonometric polynomial in the framework of Sobolev spaces of dominating mixed smoothness.
On boundedness of superposition operators in spaces of Triebel-Lizorkin type
Radial Subspaces of Besov and Lizorkin-Triebel Classes: Extended Strauss Lemma and Compactness of Embeddings.
Pointwise multipliers of Besov spaces of continuous functions.
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.
Some remarks on strong approximation by Cesàro means
An optimal symbolic calculus on Besov algebras
The characterization of radial subspaces of Besov and Lizorkin-Triebel spaces by differences
We continue our earlier investigations of radial subspaces of Besov and Lizorkin-Triebel spaces on . This time we study characterizations of these subspaces by differences.
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...
Superposition operators and functions of bounded p-variation.
We characterize the set of all functions f of R to itself such that the associated superposition operator T: g → f º g maps the class BV (R) into itself. Here BV (R), 1 ≤ p < ∞, denotes the set of primitives of functions of bounded p-variation, endowed with a suitable norm. It turns out that such an operator is always bounded and sublinear. Also, consequences for the boundedness of superposition operators defined on Besov spaces B are discussed....
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