| 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 |
| 投稿时间：2021-08-01 修订日期：2021-12-23 |
| DOI：10.3770/j.issn:2095-2651.2022.03.004 |
| 中文关键词: generalized Weinstein operator generalized Weinstein transform sobolev spaces extremal functions reproducing kernels |
| 英文关键词:generalized Weinstein operator generalized Weinstein transform sobolev spaces extremal functions reproducing kernels |
| 基金项目:Supported by Mathematics And Applications Laboratory, Faculty of Sciences, Gabes University, Tunisia. |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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