Long range scattering with Stark effect and almost periodic potentials.
Global existence of regular solutions to the Navier-Stokes equations for (v,p) coupled with the heat convection equation for θ is proved in the two-dimensional case in a bounded domain. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First an appropriate estimate is shown and next the existence is proved by the Leray-Schauder fixed point theorem. We prove the existence of solutions such that , , s>2.
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.