Extremal Functions on Generalized Weinstein Sobolev-gevrey spaces

Abstract

Note: Please see pdf for full abstract with equations. The Weinstein operator $\Delta_{W}^{\alpha,d}$, mostly referred to as theLaplace-Bessel differential operator is now known as an important operator inanalysis, because of its applications in pure and applied Mathematics,especially in Fluid Mechanics. In this paper, we consider the generalizedWeinstein operator $\Delta_{W}^{d,\alpha,n}$, we introduce and study theSobolev-Gevrey spaces associated with the generalized Weinstein operator andinvestigate their properties. Next, as application, we study the extremalfunctions on the spaces $\mathscr H_{a,\sigma}^{s,\alpha,n}(\mathbb{R}%_{+}^{d+1})$ using the theory of reproducing kernels. Mathematics Subject Classification:42B10; 42B30; 42B35; 43A32 ; 44A35; 46F12; 46E35