Geodesic
The Gradient of a Solution of the Poisson Equation in the Unit Ball and Related Operators
Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 536-545

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DOI

In this paper we determine the ${{L}^{1}}\to {{L}^{1}}$ and ${{L}^{\infty }}\to {{L}^{\infty }}$ norms of an integral operator $\mathcal{N}$ related to the gradient of the solution of Poisson equation in the unit ball with vanishing boundary data in sense of distributions.
DOI : 10.4153/CMB-2017-020-7
Mots-clés : 35J05, 47G10, Möbius transformation, Poisson equation, Newtonian potential, Cauchy transform, Bessel function 
Kalaj, David; Vujadinovic, Djordjije. The Gradient of a Solution of the Poisson Equation in the Unit Ball and Related Operators. Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 536-545. doi: 10.4153/CMB-2017-020-7
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     author = {Kalaj, David and Vujadinovic, Djordjije},
     title = {The {Gradient} of a {Solution} of the {Poisson} {Equation} in the {Unit} {Ball} and {Related} {Operators}},
     journal = {Canadian mathematical bulletin},
     pages = {536--545},
     year = {2017},
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     number = {3},
     doi = {10.4153/CMB-2017-020-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-020-7/}
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