Generalized Poisson integral and sharp estimates for harmonic and biharmonic functions in the half-space

A representation for the sharp coefficient in a pointwise estimate for the gradient of a generalized Poisson integral of a function f on Rn-1 is obtained under the assumption that f belongs to Lp. It is assumed that the kernel of the integral depends on the parameters α and β. The explicit formulas for the sharp coefficients are found for the cases p = 1, p = 2 and for some values of α, β in the case p = ∞. Conditions ensuring the validity of some analogues of the Khavinson's conjecture for the generalized Poisson integral are obtained. The sharp estimates are applied to harmonic and biharmonic functions in the half-space. © 2018 EDP Sciences.

Авторы
Kresin G.1 , Maz'ya V. 2, 3, 4
Издательство
EDP Sciences
Номер выпуска
4
Язык
Английский
Статус
Опубликовано
Номер
2018032
Том
13
Год
2018
Организации
  • 1 Department of Mathematics, Ariel University, Ariel, 40700, Israel
  • 2 Department of Mathematical Sciences, University of Liverpool, MandO Building, Liverpool, L69 3BX, United Kingdom
  • 3 Department of Mathematics, Linköping University, Linköping, 58183, Sweden
  • 4 RUDN University, 6 Miklukho-Maklay St., Moscow, 117198, Russian Federation
Ключевые слова
Biharmonic functions; Generalized Poisson integral; Harmonic functions; Sharp estimates; Two-parametric kernel
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/7134/