scholarly journals RETRACTED ARTICLE: A new application of boundary integral behaviors of harmonic functions to the least harmonic majorant

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Minghua Han ◽  
Jianguo Sun ◽  
Gaoying Xue
Keyword(s):  
Subharmonic Function ◽  
Harmonic Functions ◽  
Boundary Integral ◽  
Retracted Article ◽  
New Type ◽  
Harmonic Majorant

Abstract Our main aim in this paper is to obtain a new type of boundary integral behaviors of harmonic functions in a smooth cone. As an application, the least harmonic majorant of a nonnegative subharmonic function is also given.

scholarly journals RETRACTED ARTICLE: An augmented Riesz decomposition method for sharp estimates of certain boundary value problem

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Jiaofeng Wang ◽  
Bin Huang ◽  
Nanjundan Yamini
Keyword(s):  
Boundary Value Problem ◽  
Lower Bounds ◽  
Harmonic Functions ◽  
Decomposition Method ◽  
Integral Condition ◽  
Boundary Integral ◽  
Sharp Estimates ◽  
Riesz Decomposition ◽  
Retracted Article ◽  
Riesz Decomposition Method

AbstractIn this paper, by using an augmented Riesz decomposition method, we obtain sharp estimates of harmonic functions with certain boundary integral condition, which provide explicit lower bounds of functions harmonic in a cone. The results given here can be used as tools in the study of integral equations.

scholarly journals On Level Curves of Harmonic and Analytic Functions on Riemann Surfaces

1969 ◽  
Vol 34 ◽  
pp. 77-87
Author(s):  
Shinji Yamashitad
Keyword(s):  
Riemann Surface ◽  
Subharmonic Function ◽  
Analytic Functions ◽  
Harmonic Functions ◽  
Riemann Surfaces ◽  
Vector Lattice ◽  
Level Curves ◽  
Harmonic Majorant ◽  
Harmonic And Analytic Functions ◽  
Hyperbolic Riemann Surface

In this note we shall denote by R a hyperbolic Riemann surface. Let HP′(R) be the totality of harmonic functions u on R such that every subharmonic function | u | has a harmonic majorant on R. The class HP′(R) forms a vector lattice under the lattice operations:

scholarly journals RETRACTED ARTICLE: Growth property at infinity of harmonic functions

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Zongcai Jiang ◽  
Linbo Hou ◽  
Corchado Peixoto-de-Büyükkurt
Keyword(s):  
Harmonic Functions ◽  
Indian Acad ◽  
Growth Property ◽  
Dimensional Cone ◽  
Retracted Article

Abstract This paper gives the growth property of certain harmonic functions at infinity in an n-dimensional cone, which generalize the results obtained by Huang and Qiao (Abstr. Appl. Anal. 2012:203096, 2012), Xu et al. (Bound. Value Probl. 2013:262, 2013), Yang and Ren (Proc. Indian Acad. Sci. Math. Sci. 124(2): 175-178, 2014) and Zhao and Yamada (J. Inequal. Appl. 2014:497, 2014) to the conical case.

scholarly journals RETRACTED ARTICLE: Some new results on the boundary behaviors of harmonic functions with integral boundary conditions

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Xiaozhen Xie ◽  
Costanza T Viouonu
Keyword(s):  
Boundary Conditions ◽  
Harmonic Functions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Carleman Formula ◽  
Retracted Article ◽  
Boundary Behaviors

Abstract In this paper, using a generalized Carleman formula, we prove two new results on the boundary behaviors of harmonic functions with integral boundary conditions in a smooth cone, which generalize some recent results.

scholarly journals RETRACTED ARTICLE: Matsaev type inequalities on smooth cones

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Sheng Pang ◽  
Beatriz Ychussie
Keyword(s):  
Half Space ◽  
Harmonic Functions ◽  
Retracted Article

Abstract Our aim in this paper is to obtain Matsaev type inequalities about harmonic functions on smooth cones, which generalize the results obtained by Xu, Yang and Zhao in a half space.

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