Silke Kullmann ([email protected]) Priska Binner ([email protected]) Kirsten Rackebrandt ([email protected]) Andreas Huge ([email protected]) Georg Haltern ([email protected]) Mark Lankisch ([email protected]) Reiner Fueth ([email protected]) Eberhard von Hodenberg (eberhard.hodenberg@heart-l...

This paper focuses on the bounds of weighted multilinear Hardy operators on the product Herz spaces and the product Morrey-Herz spaces, respectively. We present a sufficient condition on the weight function that guarantees weighted multilinear Hardy operators to be bounded on the product Herz spaces. And the condition is necessary under certain assumptions. Finally, we extend the obtained resul...

Column and row operator spaces — which we denote by COL and ROW, respectively — over arbitrary Banach spaces were introduced by the first-named author; for Hilbert spaces, these definitions coincide with the usual ones. Given a locally compact group G and p, p ∈ (1,∞) with 1 p + 1 p = 1, we use the operator space structure on CB(COL(L ′ (G))) to equip the Figà-Talamanca–Herz algebra Ap(G) with ...

We study a generalisation of operator spaces modelled on Lp spaces, instead of Hilbert spaces, using the notion of p-complete boundedness, as studied by Pisier and Le Merdy. We show that the Figà-Talamanca-Herz Algebras Ap(G) becomes quantised Banach algebras in this framework, and that the cohomological notion of amenability of these algebras corresponds to amenability of the locally compact g...

A,(T) = [L9(T) ® LQ(T)]IK where K is the kernel of the convolution operator c:Lp(S>LQ(T)->C0(T) by (f®g)(y)(f* g)(y)-4*(r) is the /?-Fourier algebra which was introduced by Figa-Talamanca in [6] where it was shown that ^ ( T ) * isisometrically isomorphic to MP(T), the bounded, translation invariant, linear operators on LP(T), Herz [11] showed that AP(V) is a Banach algebra under pointwise mult...

In this paper, we establish CBMO estimates for the multilinear commutator related to the Marcinkiewicz operator in Herz and Morrey-Herz spaces.

The purpose of this paper is to study the endpoint boundedness properties of some multilinear operators related to certain integral operators on Herz and Herz type Hardy Spaces. The operators include Littlewood-Paley operator and Marcinkiewicz operator.

intimately connected with duality theory (the notation is that of [1]). In both cases the middle algebra is the closure of L(G) in the dual of the first algebra and also the predual of the third algebra (at least when G is amenable in the second case). Furthermore, the third algebra is closely connected with the multiplier algebra of the first algebra. For abelian groups, compact or discrete, V...

In this paper, the authors introduce the anisotropic Herz-Morrey spaces with two variable exponents and obtain some properties of these spaces. Subsequently as an application, the authors give some boundedness on the anisotropic Herz-Morrey spaces with two variable exponents for a class of sublinear operators, which extend some known results.