An Application of Littlewood-Paley Theory in Harmonie Analysis.
Some Applications of Grothendieck's Theory of Topological Tensor Products in Harmonie Analysis.
On the Paley-Wiener theorem.
The Fourier-Stieltjes algebra of a semisimple group
Variants of Littlewood-Paley theory.
On Representations in Banach Spaces.
Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one.
Invariant operators on function spaces on homogeneous trees
Riesz potentials and amalgams
Let be a metric space, equipped with a Borel measure satisfying suitable compatibility conditions. An amalgam is a space which looks locally like but globally like . We consider the case where the measure of the ball with centre and radius behaves like a polynomial in , and consider the mapping properties between amalgams of kernel operators where the kernel behaves like when and like when . As an application, we describe Hardy–Littlewood–Sobolev type regularity theorems...
estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III
Let be a symmetric space of the noncompact type, with Laplace–Beltrami operator , and let be the -spectrum of . For in such that , let be the operator on defined formally as . In this paper, we obtain operator norm estimates for for all , and show that these are optimal when is small and when is bounded below .
Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth
We prove that on Iwasawa AN groups coming from arbitrary semisimple Lie groups there is a Laplacian with a nonholomorphic functional calculus, not only for but also for , where 1 < p < ∞. This yields a spectral multiplier theorem analogous to the ones known for sublaplacians on stratified groups.
Contact and conformal maps on Iwasawa N groups
The action of the conformal group on may be characterized in differential geometric terms, even locally: a theorem of Liouville states that a map between domains and in whose differential is a (variable) multiple of a (variable) isometry at each point of is the restriction to of a transformation , for some in . In this paper, we consider the problem of characterizing the action of a more general semisimple Lie group on the space , where is a parabolic subgroup. We solve...
-estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. II.
A weak type (1,1) estimate for a maximal operator on a group of isometries of a homogeneous tree
We give a simple proof of a result of R. Rochberg and M. H. Taibleson that various maximal operators on a homogeneous tree, including the Hardy-Littlewood and spherical maximal operators, are of weak type (1,1). This result extends to corresponding maximal operators on a transitive group of isometries of the tree, and in particular for (nonabelian finitely generated) free groups.
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