Let and be a sequence with non-negative entries. If , denote by the infimum of those satisfying the following inequality: whenever . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). We considered this problem for certain matrix operators such as Norlund, Weighted mean, Ceasaro and Copson ma...

We developpe a direct sum decomposition for n-dual spaces. Introduction Let X be a Banach space. We will denote π0 : X → X ∗∗ and π1 : X ∗ → X∗∗∗ the canonical maps ofX and its dual space X∗ into their respective bidual spaces. According to [G] we have X∗∗∗ = Ran(π1)⊕Ker(π ∗ 0), where π∗ 0 denotes the adjoint map of π0. 1. Remark. In [G] we also saw as an application that X is reflexive if and ...

Let L be an Archimedean Riesz space with a weak order unit u. A sufficient condition under which Dedekind [σ-]completeness of the principal ideal Au can be lifted to L is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of C(X)-spaces. Similar results are obtained for the Riesz spaces Bn(T ), n = 1, 2, . . . , of all functions o...

let and be a sequence with non-negative entries. if , denote by the infimum of those satisfying the following inequality: whenever . the purpose of this paper is to give an upper bound for the norm of operator t on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). we considered this problem for certain matrix operators such as norlund, weighted mean, ceasaro and copson matrices. th...

We study the Oseen problem with rotational e ect in exterior three-dimensional domains. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces in the whole three-dimensional space. As the main tool we derive and apply an inequality of the FriedrichsPoincaré type and the theory of Calderon-Zygmund kernels in weighted spaces. For the ext...

Abstract In this paper, we study the resonance problem of a class of singular quasilinear parabolic equations with respect to its higher near-eigenvalues. Under a generalized Landesman-Lazer condition, it is proved that the resonance problem admits at least one nontrivial solution in weighted Sobolev spaces. The proof is based upon applying the Galerkin-type technique, the Brouwer’s fixedpoint ...

Given integers N n 0, we consider the least squares problem of nding the vector of coeecients ~ P with respect to a polynomial basis P N j=0 wn(zj) 2 jf(zj) ? P (zj)j 2. Here a perturbation of the values f(zj) leads to some perturbation of the coeecient vector ~ P. We denote by n the maximal magniication of relative errors, i.e., the Euclidean condition number of the underlying weighted Vanderm...

We study the Oseen problem with rotational effect in exterior three-dimensional domains. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces in the whole three-dimensional space. As the main tool we derive and apply an inequality of the FriedrichsPoincaré type and the theory of Calderon-Zygmund kernels in weighted spaces. For the ex...