The Gradient of a Solution of the Poisson Equation in the Unit Ball and Related Operators

Kalaj, David ; Vujadinovic, Djordjije

Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 536-545

Résumé

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.

Détail

DOI : 10.4153/CMB-2017-020-7

Mots-clés : 35J05, 47G10, Möbius transformation, Poisson equation, Newtonian potential, Cauchy transform, Bessel function

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