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.
A new class of linear and bounded operators is introduced. This class is more general than the classes of operators from [4], [5] and [8]. Using this class lΦ,φ we also introduce a class of locally convex spaces which is more general than the classes of the nuclear spaces [2], [3] and φ-nuclear spaces [6]. For this class of operators similar properties are established to those of the well known classes lp, lφ, lΦ and also the stability of the tensor product is proved. The stability of the tensor...