L'opérateur de temps-retard dans la théorie de la diffusion
Let be a non-negative matrix. Denote by the supremum of those that satisfy the inequality where and and also is an increasing, non-negative sequence of real numbers. If , we use instead of . In this paper we obtain a Hardy type formula for , where is a Hausdorff matrix and . Another purpose of this paper is to establish a lower bound for , where is the Nörlund matrix associated with the sequence and . Our results generalize some works of Bennett, Jameson and present authors....
In this paper we consider some matrix operators on block weighted sequence spaces . The problem is to find the lower bound of some matrix operators such as Hausdorff and Hilbert matrices on . This study is an extension of papers by G. Bennett, G.J.O. Jameson and R. Lashkaripour.
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.