GENERALIZED SOBOLEV TYPE SPACES INVOLVING THE WEINSTEIN TRANSFORM

Abstract

In this paper, the space Gp,s ω (ℝn+1+) is considered, and many properties, including completeness and inclusion, are discussed by using the theory of the Weinstein transform. It is shown that the space Sω(ℝn+1+), is dense in space Gp,s ω (ℝn+1+). The generalized Hankel potential Hk associated with the Weinstein transform is introduced, and its properties are examined. The Lp-space of all such Hankel potential, denoted by Wωm,p(ℝn+1+), is defined and it is proven that the generalized Hankel potential Ht is an isometry of Wωm,p(ℝn+1+) onto Wωm+t,p (ℝn+1+).. © Poincare Publishers.