The solution operator of the inhomogeneous Dirichlet problem in the unit ball
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- by David Kalaj and Djordjije Vujadinović
- Proc. Amer. Math. Soc. 144 (2016), 623-635
- DOI: https://doi.org/10.1090/proc/12723
- Published electronically: August 26, 2015
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Abstract:
In this paper we estimate norms of integral operator induced by the Green function related to the Poisson equation in the unit ball with vanishing boundary data.References
- Lars V. Ahlfors, Möbius transformations in several dimensions, Ordway Professorship Lectures in Mathematics, University of Minnesota, School of Mathematics, Minneapolis, Minn., 1981. MR 725161
- J. M. Anderson and A. Hinkkanen, The Cauchy transform on bounded domains, Proc. Amer. Math. Soc. 107 (1989), no. 1, 179–185. MR 972226, DOI 10.1090/S0002-9939-1989-0972226-5
- J. M. Anderson, D. Khavinson, and V. Lomonosov, Spectral properties of some integral operators arising in potential theory, Quart. J. Math. Oxford Ser. (2) 43 (1992), no. 172, 387–407. MR 1188382, DOI 10.1093/qmathj/43.4.387
- J. Arazy and D. Khavinson, Spectral estimates of Cauchy’s transform in $L^2(\Omega )$, Integral Equations Operator Theory 15 (1992), no. 6, 901–919. MR 1188786, DOI 10.1007/BF01203120
- Milutin R. Dostanić, Norm estimate of the Cauchy transform on $L^p(\Omega )$, Integral Equations Operator Theory 52 (2005), no. 4, 465–475. MR 2184599, DOI 10.1007/s00020-002-1290-9
- Milutin R. Dostanić, Estimate of the second term in the spectral asymptotic of Cauchy transform, J. Funct. Anal. 249 (2007), no. 1, 55–74. MR 2338854, DOI 10.1016/j.jfa.2007.04.007
- Milutin R. Dostanić, The properties of the Cauchy transform on a bounded domain, J. Operator Theory 36 (1996), no. 2, 233–247. MR 1432117
- S. S. Dragomir, R. P. Agarwal, and N. S. Barnett, Inequalities for beta and gamma functions via some classical and new integral inequalities, J. Inequal. Appl. 5 (2000), no. 2, 103–165. MR 1753533, DOI 10.1155/S1025583400000084
- Håkan Hedenmalm and Serguei Shimorin, Weighted Bergman spaces and the integral means spectrum of conformal mappings, Duke Math. J. 127 (2005), no. 2, 341–393. MR 2130416, DOI 10.1215/S0012-7094-04-12725-3
- Ricardo G. Durán, Marcela Sanmartino, and Marisa Toschi, Weighted a priori estimates for the Poisson equation, Indiana Univ. Math. J. 57 (2008), no. 7, 3463–3478. MR 2492240, DOI 10.1512/iumj.2008.57.3427
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR 737190, DOI 10.1007/978-3-642-61798-0
- David Kalaj, On some integral operators related to the Poisson equation, Integral Equations Operator Theory 72 (2012), no. 4, 563–575. MR 2904611, DOI 10.1007/s00020-012-1952-1
- David Kalaj, Cauchy transform and Poisson’s equation, Adv. Math. 231 (2012), no. 1, 213–242. MR 2935387, DOI 10.1016/j.aim.2012.05.003
- David Kalaj and Miroslav Pavlović, On quasiconformal self-mappings of the unit disk satisfying Poisson’s equation, Trans. Amer. Math. Soc. 363 (2011), no. 8, 4043–4061. MR 2792979, DOI 10.1090/S0002-9947-2011-05081-6
- Dmitry Khavinson, On uniform approximation by harmonic functions, Michigan Math. J. 34 (1987), no. 3, 465–473. MR 911819, DOI 10.1307/mmj/1029003626
- G. O. Thorin, Convexity theorems generalizing those of M. Riesz and Hadamard with some applications, Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 9 (1948), 1–58. MR 25529
Bibliographic Information
- David Kalaj
- Affiliation: Faculty of Mathematics, University of Montenegro, Dzordza Vašingtona bb, 81000 Podgorica, Montenegro
- MR Author ID: 689421
- Djordjije Vujadinović
- Affiliation: Faculty of Mathematics, University of Montenegro, Dzordza Vašingtona bb, 81000 Podgorica, Montenegro
- MR Author ID: 1019454
- Email: djordjijevuj@t-com.me
- Received by editor(s): October 9, 2014
- Received by editor(s) in revised form: January 12, 2015
- Published electronically: August 26, 2015
- Communicated by: Franc Forstneric
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 623-635
- MSC (2010): Primary 35J05; Secondary 47G10
- DOI: https://doi.org/10.1090/proc/12723
- MathSciNet review: 3430840