On the Existence of Angular Boundary Values for Polyharmonic Functions in the Unit Ball

2018 ◽  
Vol 234 (3) ◽  
pp. 362-368
Author(s):  
M. Ya. Mazalov
Keyword(s):  
Unit Ball ◽  
Boundary Values ◽  
Polyharmonic Functions ◽  
Angular Boundary

scholarly journals Spherical means of super-polyharmonic functions in the unit ball

2014 ◽  
Vol 44 (2) ◽  
pp. 235-245
Author(s):  
Toshihide Futamura ◽  
Yoshihiro Mizuta ◽  
Takao Ohno
Keyword(s):  
Unit Ball ◽  
Spherical Means ◽  
Polyharmonic Functions

Riesz decomposition for super-polyharmonic functions in the punctured unit ball

2014 ◽  
Vol 51 (1) ◽  
pp. 1-16
Author(s):  
Toshihide Futamura ◽  
Yoshihiro Mizuta ◽  
Takao Ohno
Keyword(s):  
Fundamental Solution ◽  
Unit Ball ◽  
Growth Condition ◽  
Decomposition Theorem ◽  
Polyharmonic Functions ◽  
Riesz Decomposition ◽  
Surface Integrals

We consider a Riesz decomposition theorem for super-polyharmonic functions satisfying certain growth condition on surface integrals in the punctured unit ball. We give a condition that super-polyharmonic functions u have the bound \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$u\left( x \right) = O\left( {\mathcal{R}_2 \left( x \right)} \right),$$ \end{document} where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{R}_2$$ \end{document} denotes the fundamental solution for −Δu in ℝn.

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