Global Journal of Pure and Applied Mathematics
  • Year: 2007
  • Volume: 3
  • Issue: 1

Almost Periodic Functions with Values in p-Fréchet Spaces, 0 < p < 1

  • Author:
  • Sorin G. Gal1, Gaston M. N'Guérékata2
  • Total Page Count: 15
  • Page Number: 89 to 103

1Department of Mathematics University of Oradea, Romania Str. Universitatii No. 1 410087 Oradea, Romania. E-mail: galso@uoradea.ro

2Department of Mathematics Morgan State University Baltimore, MD 21251, USA. E-mail: gnguerek@jewel.morgan.edu

1991 Mathematics Subject Classification: 43A60, 34C35, 34G10.

Abstract

In this paper we develop a theory of almost periodic functions with values in the nonlocally convex spaces called p-Fréchet spaces, 0 < p < 1, including the lp, Lp spaces and the Hardy space Hp. Although the p-norm, 0 < p < 1, has not all the properties of an usual norm, the majority of main properties of almost periodic functions with values in Banach spaces are extended to this case. Some applications to differential equations and to dynamical systems in p-Fréchet spaces, 0 < p < 1, are given.

Keywords

p-Fréchet space, almost periodic functions, functions with values in p-Fréchet spaces, 0 < p < 1