Lipschitz continuity for weighted harmonic functions in the unit disc

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Lipschitz continuity for weighted harmonic functions in the unit disc. / Olofsson, Anders.

I: Complex Variables and Elliptic Equations, Vol. 65, Nr. 10, 2020, s. 1630-1660.

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TY - JOUR

T1 - Lipschitz continuity for weighted harmonic functions in the unit disc

AU - Olofsson, Anders

PY - 2020

Y1 - 2020

N2 - We study membership in Lipschitz classes (Formula presented.) for a class of α-harmonic functions in the open unit disc (Formula presented.) in the complex plane. From earlier work by Olofsson and Wittsten we know that such an α-harmonic function u is the α-harmonic Poisson integral (Formula presented.) of its boundary value function f on the unit circle (Formula presented.). We determine when the Poisson integral (Formula presented.) belongs to a Lipschitz class (Formula presented.) for the unit disc.

AB - We study membership in Lipschitz classes (Formula presented.) for a class of α-harmonic functions in the open unit disc (Formula presented.) in the complex plane. From earlier work by Olofsson and Wittsten we know that such an α-harmonic function u is the α-harmonic Poisson integral (Formula presented.) of its boundary value function f on the unit circle (Formula presented.). We determine when the Poisson integral (Formula presented.) belongs to a Lipschitz class (Formula presented.) for the unit disc.

KW - D. Khavinson

KW - Fourier multiplier

KW - harmonic function

KW - Lipschitz continuity

KW - Poisson integral

KW - Primary: 31A05

KW - Secondary: 35J25

U2 - 10.1080/17476933.2019.1669572

DO - 10.1080/17476933.2019.1669572

M3 - Article

AN - SCOPUS:85073994292

VL - 65

SP - 1630

EP - 1660

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

IS - 10

ER -