| New Sobolev-Weinstein Spaces and Applications |
| Received:August 01, 2021 Revised:December 23, 2021 |
| Key Words:
generalized Weinstein operator generalized Weinstein transform sobolev spaces extremal functions reproducing kernels
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| Fund Project:Supported by Mathematics And Applications Laboratory, Faculty of Sciences, Gabes University, Tunisia. |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.03.004 |
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