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.
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 
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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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