Hassen BEN MOHAMED,Youssef BETTAIBI.New Sobolev-Weinstein Spaces and Applications[J].数学研究及应用,2022,42(3):247~260
New Sobolev-Weinstein Spaces and Applications
New Sobolev-Weinstein Spaces and Applications

DOI：10.3770/j.issn:2095-2651.2022.03.004

 作者 单位 Hassen BEN MOHAMED Department of Mathematics, Faculty of Sciences, Gabes University, Tunisia Youssef BETTAIBI Department of Mathematics, Faculty of Sciences, Gabes University, Tunisia

In this paper, we consider the generalized Weinstein operator $\Delta_{W}^{d,\alpha,n}$, we introduce new Sobolev-Weinstein spaces denoted $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1}),$ $s\in\mathbb{R},$ associated with the generalized Weinstein operator and we investigate their properties. Next, as application, we study the extremal functions on the spaces $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1})$ using the theory of reproducing kernels.

In this paper, we consider the generalized Weinstein operator $\Delta_{W}^{d,\alpha,n}$, we introduce new Sobolev-Weinstein spaces denoted $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1}),$ $s\in\mathbb{R},$ associated with the generalized Weinstein operator and we investigate their properties. Next, as application, we study the extremal functions on the spaces $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1})$ using the theory of reproducing kernels.