Opérateurs pseudo-différentiels sur certains groupes totalement discontinus
Operator Figà-Talamanca-Herz algebras
Let G be a locally compact group. We use the canonical operator space structure on the spaces for p ∈ [1,∞] introduced by G. Pisier to define operator space analogues of the classical Figà-Talamanca-Herz algebras . If p ∈ (1,∞) is arbitrary, then and the inclusion is a contraction; if p = 2, then OA₂(G) ≅ A(G) as Banach spaces, but not necessarily as operator spaces. We show that is a completely contractive Banach algebra for each p ∈ (1,∞), and that completely contractively for amenable...
Operator Segal algebras in Fourier algebras
Let G be a locally compact group, A(G) its Fourier algebra and L¹(G) the space of Haar integrable functions on G. We study the Segal algebra S¹A(G) = A(G) ∩ L¹(G) in A(G). It admits an operator space structure which makes it a completely contractive Banach algebra. We compute the dual space of S¹A(G). We use it to show that the restriction operator , for some non-open closed subgroups H, is a surjective complete quotient map. We also show that if N is a non-compact closed subgroup, then the averaging...
Operators associated with representations of amenable groups singular integrals induced by ergodic flows, the rotation method and multipliers
Operators on VN(G) commuting with A(G)
Operators which commute with convolutions on subspaces of
Operator-valued version of conditionally free product
We present an operator-valued version of the conditionally free product of states and measures, which in the scalar case was studied by Bożejko, Leinert and Speicher. The related combinatorics and limit theorems are provided.
Optimal boundedness of central oscillating multipliers on compact Lie groups
Fefferman-Stein, Wainger and Sjölin proved optimal boundedness for certain oscillating multipliers on . In this article, we prove an analogue of their result on a compact Lie group.
Orbit closures of generic unipotent flows on homogeneous spaces of SL (3, IR).
Order convolution and vector-valued multipliers
Let I = (0,∞) with the usual topology. For x,y ∈ I, we define xy = max(x,y). Then I becomes a locally compact commutative topological semigroup. The Banach space L¹(I) of all Lebesgue integrable functions on I becomes a commutative semisimple Banach algebra with order convolution as multiplication. A bounded linear operator T on L¹(I) is called a multiplier of L¹(I) if T(f*g) = f*Tg for all f,g ∈ L¹(I). The space of multipliers of L¹(I) was determined by Johnson and Lahr. Let X be a Banach space...
Order Isomorphisms of Fourier-Stieltjes Algebras.
Orthogonal symmetric pairs and the Rouvière isomorphism. (Paires symétriques orthogonales et isomorphisme de Rouvière.)
Oscillating multipliers on noncompact symmetric spaces.
Oscillating multipliers on the Heisenberg group
Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator is bounded on for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.
Outer measures and weak type estimates of Hardy-Littlewood maximal operators.
-adic -functions attached to characters of -power order
-adic Whittaker functions and vector bundles on flag manifolds
Pairings, duality, amenability and bounded cohomology
We give a new perspective on the homological characterizations of amenability given by Johnson & Ringrose in the context of bounded cohomology and by Block & Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterizations. We apply these ideas to give a new proof of non-vanishing for the bounded cohomology of a free group.
Paley-Wiener Type Theorems on Harmonic Extensions of H-Type Groups.
P-Amenable Locally Compact Groups.