be any sequence of signs .

In this paper we present some results on convergence and summability of oneand multi-dimensional trigonometric andWalsh-Fourier series. The Fejér and Cesàro summability methods are investigated. We will prove that the maximal operator of the summability means is bounded from the corresponding classical or martingale Hardy space Hp to Lp for some p > p0. For p = 1 we obtain a weak type inequalit...

We have established a relation between θ−|R,pn|k and θ−|R,qn|k summability methods, k > 1, which generalizes a result of Sunouchi (1949) on |R,pn| and |R,qn| summability methods.

The concept of a spectral triple (unbounded Fredholm module) due to A.Connes ([Co1]) is a natural noncommutative generalisation of a notion of a compact manifold, with certain summability properties corresponding in the classical case to the dimension of the manifold. Recently E.Christensen and C. Ivan established the existence of spectral triples on arbitrary AF algebras ([CI]). In this note w...

We provide a new separation-based proof of the domination theorem for (q, 1)-summing operators. This result gives celebrated factorization Pisier operators acting in C(K)-spaces. As far as we know, none known versions uses separation argument presented here, which is essentially same that proves Pietsch Domination Theorem p-summing Based on this proof, propose an equivalent formulation main sum...

in this paper,  we determine necessary and sufficient tauberian conditions under which convergence in pringsheim's sense of a double sequence of fuzzy numbers follows from its $(c,1,1)$ summability. these conditions are satisfied if the double sequence of fuzzy numbers is slowly oscillating in different senses. we also construct some interesting double sequences of fuzzy numbers.

We present two explicit combinatorial constructions of finitely summable reduced “Gamma”-elements $\gamma\_r\in KK(C^\*\_r(\Gamma),\mathbb{C})$ for any word-hyperbolic group $(\Gamma,S)$ and obtain summability bounds them in terms the cardinality generating set $S\subset\Gamma$ hyperbolicity constant associated Cayley graph.

p . It follows that inequality (1.2) holds for any a ∈ lp when U1/p ≥ ||C||p,p and fails to hold for some a ∈ lp when U1/p < ||C||p,p. Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cn,k = 1/n, k ≤ n and 0 otherwise, is bounded on l p and has norm ≤ p/(p−1). (The norm is in fact p/(p− 1).) We say a matrix A = (an,k) is a lower triangular matrix if an,k = 0 for n < k...