Sağir, Birsen; Güngör, Nihan

Let R be set of all real numbers, N be the set of all natural numbers and N2 = N×N. In this paper, we define the superposition operator Pg where g: N2×R → R by Pg ((xks)) = g(k,s,xks) for all real double sequence (xks). Chew & Lee [4] and Petranuarat & Kemprasit [11] have characterized Pg: c0 → l1 and Pg: c0 → lq where 1 ≤ q < ∞, respectively. The main aim of this paper is to construct the necessary and sufficient conditions for the boundedness and continuity of Pg: Cr0 → L1 and Pg: Cr0 → Lp where 1≤ p< ∞.

Güngör, Nihan; Sağir, Birsen

Let 1≤q, p < ∞ and υ,w be Beurling's weight functions on Rd. In this article we deal with harmonic properties of intersection space Aq,pk,υ,w (Rd) = Lqυ (Rd) ∩ Wp,wk (Rd) defined by aid of weighted Lebesgue space Lqυ (Rd) and weighted Sobolev space Wp,wk (Rd). We research the inclusions and inequalities between the spaces Aq,pk,υ,w (Ω) where Ω ⊂ Rd be an open set. Finally, we proved that the spaces M (A1,pk,w (Rd), L1w (Rd)) can be identified with the weighted spaces of bounded measures Mw (Rd).