Semigroups of operators commuting with translations
We survey some recent results on functional calculus for generators of holomorphic semigroups, which have been obtained using versions of fractional derivation of Riemann-Liouville or Weyl type. Such a calculus allows us to give tight estimates even in concrete L¹ examples.
Let I = [0, 1] be the compact topological semigroup with max multiplication and usual topology. C(I), , 1 ≤ p ≤ ∞, are the associated Banach algebras. The aim of the paper is to characterise and their preduals.
Consider I = [0,1] as a compact topological semigroup with max multiplication and usual topology, and let , be the associated algebras. The aim of this paper is to study the spaces , r > p, and their preduals.
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.
We study spectral multipliers for a distinguished Laplacian on certain groups of exponential growth. We obtain a stronger optimal version of the results proved in [CGHM] and [A].
Soit , l’espace de Banach des fonctions continues sur qui sont parties réelles de fonctions de l’algèbre du disque . On étudie les ensembles de de synthèse pour et l’algèbre des multiplicateurs de . On en déduit des théorèmes d’approximation dans par des produits de Blaschke.
It is well known that in a free group , one has , where E is the set of all the generators. We show that the (completely) bounded multiplier norm of any set satisfying the Leinert condition depends only on its cardinality. Consequently, based on a result of Wysoczański, we obtain a formula for .
Let G be a locally compact group, let (φ,ψ) be a complementary pair of Young functions, and let and be the corresponding Orlicz spaces. Under some conditions on φ, we will show that for a Banach -submodule X of , the multiplier space is a dual Banach space with predual , where the closure is taken in the dual space of . We also prove that if is a Δ₂-regular N-function, then , the space of convolutors of , is identified with the dual of a Banach algebra of functions on G under pointwise...
By combining some results of C. S. Herz on the Fourier algebra with the notion of contractions of Lie groups, we prove theorems which allow transference of multipliers either from the Lie algebra or from the Cartan motion group associated to a compact Lie group to the group itself.