Continuity of Superposition Operators on the Double Sequence Spaces Lp

Abstract

In this paper, we define the superposition operator P<inf>g</inf> where g : N2 * R → R by P<inf>g</inf> ((x<inf>ks</inf>)) =<inf>g</inf> (k; s; x<inf>ks</inf>) for all real double sequence (x<inf>ks</inf>). Chew & Lee [4] and Petranuarat & Kemprasit [7] have characterized P<inf>g</inf> : l<inf>p</inf> → l<inf>1</inf> and P<inf>g</inf> : l<inf>p</inf> → l<inf>q</inf> where 1 ≤ p; q < ∞, respectively. The main goal of this paper is to construct the necessary and sucient conditions for the continuity of P<inf>g</inf> : L<inf>p</inf> → L<inf>1</inf> and P<inf>g</inf> : L<inf>p</inf> → L<inf>q</inf> where 1 _ p; q < ∞. © 2015, University of Nis. All rights reserved.