using a generalized spherical mean operator, we obtain a generalization of titchmarsh&apos;s theorem for the dunkl transform for functions satisfying the (&apos;; p)-dunkl lipschitz condition in the space lp(rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.

A classification of weakly compact multiplication operators on L(Lp), 1 < p < ∞, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of lp-strictly singular operators, and we also investigate the structure of general lp-strictly singular operators on Lp. The main result is that if an operator T on Lp, 1 < p < 2, is lp-strictly singular ...

Given a sequence of positive Hermitian holomorphic line bundles (Lp,hp) on Kähler manifold X, we establish the asymptotic expansion Bergman kernel space global sections Lp, under natural convergence assumption curvatures c1(Lp,hp). We then apply this to study distribution common zeros random sequences m-tuples Lp as p→+∞.

We show that the Hilbert space is coarsely embeddable into any lp for 1 ≤ p < ∞. In particular, this yields new characterizations of embeddability of separable metric spaces into the Hilbert space. Coarse embeddings were defined by M. Gromov [Gr] to express the idea of inclusion in the large scale geometry of groups. G. Yu showed later that the case when a finitely generated group with a word l...

The idea of replacing functions by linear operators, the process of quantization, goes back to the foundations of quantum mechanics and has a great impact in mathematics. This applies for instance to representation theory, operator algebra, noncommutative geometry, quantum and free probability or operator space theory. The quantization of measure theory leads to the theory of Lp spaces defined ...

Volterra difference equations arise in the mathematical modeling of some real phenomena, and also in numerical schemes for solving differential and integral equations (cf. [7, 8] and the references therein). One of the basic methods in the theory of stability and boundedness of Volterra difference equations is the direct Lyapunov method (see [1, 3, 4] and the references therein). But finding th...

The purpose of this paper is to establish Lp error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere. In particular, the Bernstein inequality estimates Lp Bessel-potential Sobolev norms of functions in this space in terms of the minimal separation and the Lp norm of the functi...