A Riesz-Fejér type inequality for harmonic functions

2021 ◽  
pp. 125812
Author(s):  
Suman Das ◽  
Anbareeswaran Sairam Kaliraj
Keyword(s):  
Harmonic Functions ◽  
Type Inequality

scholarly journals SCHWARZ LEMMA FOR HOLOMORPHIC MAPPINGS IN THE UNIT BALL

2017 ◽  
Vol 60 (1) ◽  
pp. 219-224 ◽  
Author(s):  
DAVID KALAJ
Keyword(s):  
Unit Ball ◽  
Harmonic Functions ◽  
Type Inequality ◽  
Holomorphic Mappings ◽  
Schwarz Lemma ◽  
Complex Spaces

AbstractIn this note, we establish a Schwarz–Pick type inequality for holomorphic mappings between unit balls Bn and Bm in corresponding complex spaces. We also prove a Schwarz-Pick type inequality for pluri-harmonic functions.

Positive Harmonic Functions and Complete Metrics

1989 ◽  
Vol 32 (3) ◽  
pp. 286-297 ◽  
Author(s):  
David A. Herron ◽  
Joel L. Schiff
Keyword(s):  
Harmonic Functions ◽  
Type Inequality ◽  
Rate Of Growth ◽  
Harnack Type Inequality ◽  
Simply Connected ◽  
Complete Metrics ◽  
Positive Harmonic Functions

AbstractWe introduce the class of Harnack domains in which a Harnack type inequality holds for positive harmonic functions with bounds given in terms of the distance to the domain's boundary. We give conditions connecting Harnack domains with several different complete metrics. We characterize the simply connected plane domains which are Harnack and discuss associated topics. We extend classical results to Harnack domains and give applications concerning the rate of growth of various functions defined in Harnack domains. We present a perhaps new characterization for quasidisks.

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