Resolventenkerne, Carleman-Operatoren in LP-Räumen und Hille-Tamarkin-Operatoren.
Riemannian analogue of a Paley-Zygmund theorem
Riesz meets Sobolev
We show that the boundedness, p > 2, of the Riesz transform on a complete non-compact Riemannian manifold with upper and lower Gaussian heat kernel estimates is equivalent to a certain form of Sobolev inequality. We also characterize in such terms the heat kernel gradient upper estimate on manifolds with polynomial growth.
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...