Function Spaces of Sobolev Type on Riemannian Symmetric Manifolds.
Vector-Valued Fourier Multipliers on Symmetric Spaces of the Noncompact Type.
Besov spaces on symmetric manifolds—the atomic decomposition
We give the atomic decomposition of the inhomogeneous Besov spaces defined on symmetric Riemannian spaces of noncompact type. As an application we get a theorem of Bernstein type for the Helgason-Fourier transform.
Remark on spline unconditional bases in
Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions.
Let H be a closed subgroup of the group of rotation of Rn. The subspaces of distributions of Besov-Lizorkin-Triebel type invariant with respect to natural action of H are investigated. We give sufficient and necessary conditions for the compactness of the Sobolev-type embeddings. It is also proved that H-invariance of function implies its decay properties at infinity as well as the better local smoothness. This extends the classical Strauss lemma. The main tool in our investigations is an adapted...
Besov spaces and function series on Lie groups (II).
In this paper we investigate the absolute convergence in the sup-norm of two-sided Harish-Chandra's Fourier series of functions belonging to Zygmund-Hölder spaces defined on non-compact connected Lie groups. [Part I of the article in MR1240211].
Approximation and entropy numbers of compact Sobolev embeddings
The aim of the paper is twofold. First we give a survey of some recent results concerning the asymptotic behavior of the entropy and approximation numbers of compact Sobolev embeddings. Second we prove new estimates of approximation numbers of embeddings of weighted Besov spaces in the so called limiting case.
On Besov spaces and absolute convergence of the Fourier transform on Heisenberg groups
In this paper the absolute convergence of the group Fourier transform for the Heisenberg group is investigated. It is proved that the Fourier transform of functions belonging to certain Besov spaces is absolutely convergent. The function spaces are defined in terms of the heat semigroup of the full Laplacian of the Heisenberg group.
Besov spaces and function series on Lie groups
In the paper we investigate the absolute convergence in the sup-norm of Harish-Chandra's Fourier series of functions belonging to Besov spaces defined on non-compact connected Lie groups.
Radial Subspaces of Besov and Lizorkin-Triebel Classes: Extended Strauss Lemma and Compactness of Embeddings.
Remark on borderline traces of Besov and Triebel-Lizorkin spaces on noncompact hypersurfaces
We investigate borderline traces of Besov and Triebel-Lizorkin spaces. The function spaces are defined on noncompact Riemannian manifolds with bounded geometry. We described spaces of traces on noncompact submanifolds that are also of bounded geometry.
Embeddings of Besov-Morrey spaces on bounded domains
We study embeddings of spaces of Besov-Morrey type, , where is a bounded domain, and obtain necessary and sufficient conditions for the continuity and compactness of . This continues our earlier studies relating to the case of . Moreover, we also characterise embeddings into the scale of spaces or into the space of bounded continuous functions.
Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, I.
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.
Besov spaces and function series on Lie groups.
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