New Sobolev-Weinstein Spaces and Applications
Received:August 01, 2021  Revised:December 23, 2021
Key Word: generalized Weinstein operator   generalized Weinstein transform   sobolev spaces   extremal functions   reproducing kernels  
Fund ProjectL:Supported by Mathematics And Applications Laboratory, Faculty of Sciences, Gabes University, Tunisia.
Author NameAffiliation
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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      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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