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Besov spaces on symmetric manifolds—the atomic decomposition

Leszek Skrzypczak (1997)

Studia Mathematica

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.

BGG sequences on spheres

Petr Somberg (2000)

Commentationes Mathematicae Universitatis Carolinae

BGG sequences on flat homogeneous spaces are analyzed from the point of view of decomposition of appropriate representation spaces on irreducible parts with respect to a maximal compact subgroup, the so called K -types. In particular, the kernels and images of all standard invariant differential operators (including the higher spin analogs of the basic twistor operator), i.e. operators appearing in BGG sequences, are described.

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