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

Published online by Cambridge University Press:  20 November 2018

David Kalaj  and
Djordjije Vujadinovic
David Kalaj
Affiliation:
Faculty of Mathematics, University of Montenegro, Dzordza Vašingtona bb, 81000 Podgorica, Montenegro. e-mail: davidkalaj@gmail.com e-mail: djordjijevuj@t-com.me
Djordjije Vujadinovic
Affiliation:
Faculty of Mathematics, University of Montenegro, Dzordza Vašingtona bb, 81000 Podgorica, Montenegro. e-mail: davidkalaj@gmail.com e-mail: djordjijevuj@t-com.me
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Abstract

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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.

Keywords

35J0547G10Möbius transformationPoisson equationNewtonian potentialCauchy transformBessel function
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 3 , 01 September 2017 , pp. 536 - 545
Copyright
Copyright © Canadian Mathematical Society 2017

References

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