Herz-type Besov spaces on locally compact Vilenkin groups.
We derive various integral representation formulas for a function minus a polynomial in terms of vector field gradients of the function of appropriately high order. Our results hold in the general setting of metric spaces, including those associated with Carnot-Carathéodory vector fields, under the assumption that a suitable to Poincaré inequality holds. Of particular interest are the representation formulas in Euclidean space and stratified groups, where polynomials exist and to Poincaré...
The aim of this paper is to extend the study of Riesz transforms associated to Dunkl Ornstein-Uhlenbeck operator considered by A. Nowak, L. Roncal and K. Stempak to higher order.
Continuous actions of topological groups on compact Hausdorff spaces X are investigated which induce almost periodic functions in the corresponding commutative C*-algebra. The unique invariant mean on the group resulting from averaging allows one to derive a C*-valued inner product and a Hilbert C*-module which serve as an environment to describe characteristics of the group action. For Lyapunov stable actions the derived invariant mean is continuous on X for any ϕ ∈ C(X), and the induced C*-valued...
The aim of this paper is to show that the integral and derivative operators defined by local regularities are homeomorphisms for generalized Besov and Triebel-Lizorkin spaces with local regularities. The underlying geometry is that of homogeneous type spaces and the functions defining local regularities belong to a larger class of growth functions than the potentials tα, related to classical fractional integral and derivative operators and Besov and Triebel-Lizorkin spaces.
This paper considers the Lipschitz subalgebras of a homogeneous algebra on the circle. Interpolation space theory is used to derive estimates for the multiplier norm on closed primary ideals in , . From these estimates the Ditkin and Analytic Ditkin conditions for follow easily. Thus the well-known theory of (regular) Banach algebras satisfying the Ditkin condition applies to as does the theory developed in part I of this series which requires the Analytic Ditkin condition.Examples are discussed...
Let S be a Rees semigroup, and let ℓ¹(S) be its convolution semigroup algebra. Using Morita equivalence we show that bounded Hochschild homology and cohomology of ℓ¹(S) are isomorphic to those of the underlying discrete group algebra.
Let A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism φ: A → B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and φ) are given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms from...
We prove that, for a distinguished laplacian on an Iwasawa AN group corresponding to a complex semisimple Lie group, a Hörmander type multiplier theorem holds. Our argument is based on Littlewood-Paley theory.
Let X be a Polish space, and let be a sequence of hereditary subsets of K(X) (the space of compact subsets of X). We give a general criterion which allows one to decide whether is a true subset of K(X). We apply this criterion to show that several natural families of thin sets from harmonic analysis are true .
For every closed subset C in the dual space of the Heisenberg group we describe via the Fourier transform the elements of the hull-minimal ideal j(C) of the Schwartz algebra and we show that in general for two closed subsets of the product of and is different from .