Polynomial Control on Weighted Stability Bounds and Inversion Norms of Localized Matrices on Simple Graphs

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

ON lp NORMS OF WEIGHTED MEAN MATRICES

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...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Weighted Lp-stability For Localized Infinite Matrices

This dissertation originates from a classical result that the `-stability of the convolution operator associated with a summable sequence are equivalent to each other for 1 ≤ p ≤ ∞. This dissertation is motivated by the recent result by C. E. Shin and Q. Sun (Journal of Functional Analysis, 256(2009), 2417–2439), where the `-stability of infinite matrices in the Gohberg-Baskakov-Sjöstrand class...

Lower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...