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GENERALIZED POISSON INTEGRAL AND SHARP ESTIMATES FOR HARMONIC AND BIHARMONIC FUNCTIONS IN THE HALF-SPACE
Ariel Univ, Israel.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. Univ Liverpool, England; RUDN Univ, Russia.
2018 (English)In: Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, E-ISSN 1760-6101, Vol. 13, no 4, article id UNSP 37Article in journal (Refereed) Published
Abstract [en]

A representation for the sharp coefficient in a pointwise estimate for the gradient of a generalized Poisson integral of a function f on f(n-1) is obtained under the assumption that f belongs to L-p. It is assumed that the kernel of the integral depends on the parameters alpha and beta. The explicit formulas for the sharp coefficients are found for the cases p = 1, p = 2 and for some values of alpha, beta in the case p = infinity. Conditions ensuring the validity of some analogues of the Khavinsons conjecture for the generalized Poisson integral are obtained. The sharp estimates are applied to harmonic and biharmonic functions in the half-space.

Place, publisher, year, edition, pages
EDP SCIENCES S A , 2018. Vol. 13, no 4, article id UNSP 37
Keywords [en]
Generalized Poisson integral; two-parametric kernel; sharp estimates; harmonic functions; biharmonic functions
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-152638DOI: 10.1051/mmnp/2018032ISI: 000447914100005OAI: oai:DiVA.org:liu-152638DiVA, id: diva2:1262064
Note

Funding Agencies|Ministry of Education and Science of the Russian Federation [02.a03.21.0008]

Available from: 2018-11-09 Created: 2018-11-09 Last updated: 2018-12-03

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Mazya, Vladimir
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