Some inequalities for gradients of harmonic functions
Abstract
For a function u(x, y) harmonic in the upper half-plane y>0 and represented by the Poisson integral of a function v(t) ∈ L 2 (−∞,∞), we prove that the inequality gradu(x,y)|2 ⩽ 14π3 ∞∫−∞v2(t)dt is true. A similar inequality is obtained for a function harmonic in a disk.
Published
25.08.1997
How to Cite
Grigor’ev, Y. A. “Some Inequalities for Gradients of Harmonic Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 49, no. 8, Aug. 1997, pp. 1135–1136, https://umj.imath.kiev.ua/index.php/umj/article/view/5106.
Issue
Section
Short communications