scholarly journals Free pluriharmonic functions on noncommutative polyballs

2016 ◽  
Vol 9 (5) ◽  
pp. 1185-1234 ◽  
Author(s):  
Gelu Popescu
Keyword(s):  
Pluriharmonic Functions

Integral Representations and Continuous Projectors in Some Spaces of Analytic and Pluriharmonic Functions

2008 ◽  
Vol 15 (4) ◽  
pp. 739-752
Author(s):  
Gigla Oniani ◽  
Lamara Tsibadze
Keyword(s):  
Integral Representations ◽  
Fractional Integrals ◽  
Boundary Values ◽  
Pluriharmonic Functions

Abstract We consider analytic and pluriharmonic functions belonging to the classes 𝐵𝑝(Ω) and 𝑏𝑝(Ω) and defined in the ball . The theorems established in the paper make it possible to obtain some integral representations of functions of the above-mentioned classes. The existence of bounded projectors from the space 𝐿(ρ, Ω) into the space 𝐵𝑝(Ω) and from the space 𝐿(ρ, Ω) into the space 𝑏𝑝(Ω) is proved. Also, consideration is given to the existence of boundary values of fractional integrals of functions of the spaces 𝐵𝑝(Ω) and 𝑏𝑝(Ω).

Some Extreme Rays of the Positive Pluriharmonic Functions

1979 ◽  
Vol 31 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Frank Forelli
Keyword(s):  
Unit Ball ◽  
Extreme Point ◽  
Extreme Points ◽  
Holomorphic Functions ◽  
Open Unit ◽  
Compact Open Topology ◽  
Open Unit Ball ◽  
Pluriharmonic Functions ◽  
Image Position ◽  
Extreme Rays

1.1. We will denote by B the open unit ball in Cn, and we will denote by H(B) the class of all holomorphic functions on B. LetThus N(B) is convex (and compact in the compact open topology). We think that the structure of N(B) is of interest and importance. Thus we proved in [1] that if(1.1)if(1.2)and if n≧ 2, then g is an extreme point of N(B). We will denote by E(B) the class of all extreme points of N(B). If n = 1 and if (1.2) holds, then as is well known g ∈ E(B) if and only if(1.3)

Pluriharmonic functions on abstract CR manifolds

1996 ◽  
Vol 170 (1) ◽  
pp. 377-394 ◽  
Author(s):  
C. Medori ◽  
M. Nacinovich
Keyword(s):  
Cr Manifolds ◽  
Pluriharmonic Functions
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