NEW SOBOLEV-WEINSTEIN SPACES AND APPLICATIONS
Received:August 01, 2021  Revised:December 20, 2021
Key Word: Generalized Weinstein operator   Generalized Weinstein transform   Sobolev Spaces   Extremal functions   Reproducing kernels.  
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Hassen Houcine BEN MOHAMED Faculty of Sciences of Gabes Tunisia Faculty of Sciences of Gabes, city Ryadh, Zrig 6072 Tunisia
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Abstract:
      In this paper, we consider the generalized Weinstein operator Δ_{W}^{d,α,n}, we introduce new Sobolev-Weinstein spaces denoted [mathscr]\mathscrH_{α,d,n}^{s}(R?^{d+1}), s∈R, associated with the generalized Weinstein operator and we investigate their properties. Next, as application, we study the extremal functions on the spaces [mathscr]\mathscrH_{α,d,n}^{s}(R?^{d+1}) using the theory of reproducing kernels.
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