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Lower bound and upper bound of operators on block weighted sequence spaces

Rahmatollah Lashkaripour, Gholomraza Talebi (2012)

Czechoslovak Mathematical Journal

Let A = ( a n , k ) n , k 1 be a non-negative matrix. Denote by L v , p , q , F ( A ) the supremum of those L that satisfy the inequality A x v , q , F L x v , p , F , where x 0 and x l p ( v , F ) and also v = ( v n ) n = 1 is an increasing, non-negative sequence of real numbers. If p = q , we use L v , p , F ( A ) instead of L v , p , p , F ( A ) . In this paper we obtain a Hardy type formula for L v , p , q , F ( H μ ) , where H μ is a Hausdorff matrix and 0 < q p 1 . Another purpose of this paper is to establish a lower bound for A W N M v , p , F , where A W N M is the Nörlund matrix associated with the sequence W = { w n } n = 1 and 1 < p < . Our results generalize some works of Bennett, Jameson and present authors....

Lower bounds for matrices on block weighted sequence spaces. I

R. Lashkaripour, D. Foroutannia (2009)

Czechoslovak Mathematical Journal

In this paper we consider some matrix operators on block weighted sequence spaces l p ( w , F ) . The problem is to find the lower bound of some matrix operators such as Hausdorff and Hilbert matrices on l p ( w , F ) . This study is an extension of papers by G. Bennett, G.J.O. Jameson and R. Lashkaripour.

LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators

Karapetyants, Alexey, Karasev, Denis, Nogin, Vladimir (2005)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15.We obtain the Lp → Lq - estimates for the fractional acoustic potentials in R^n, which are known to be negative powers of the Helmholtz operator, and some related operators. Some applications of these estimates are also given.* This paper has been supported by Russian Fond of Fundamental Investigations under Grant No. 40–01–008632 a.

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