Angular derivatives and boundary values of H(b) spaces of unit ball of ℂn

2020 ◽  
Vol 66 (2) ◽  
pp. 226-237
Author(s):  
Sibel Şahin
Keyword(s):  
Unit Ball ◽  
Boundary Values ◽  
Angular Derivatives

Estimates for Convex Integral Means of Harmonic Functions

2013 ◽  
Vol 57 (3) ◽  
pp. 619-630
Author(s):  
Dimitrios Betsakos
Keyword(s):  
Harmonic Function ◽  
Unit Ball ◽  
Unit Sphere ◽  
Harmonic Functions ◽  
Integrable Function ◽  
Right Hemisphere ◽  
Boundary Values ◽  
Integral Means ◽  
Decreasing Rearrangement ◽  
The Right

AbstractWe prove that if f is an integrable function on the unit sphere S in ℝn, g is its symmetric decreasing rearrangement and u, v are the harmonic extensions of f, g in the unit ball , then v has larger convex integral means over each sphere rS, 0 < r < 1, than u has. We also prove that if u is harmonic in with |u| < 1 and u(0) = 0, then the convex integral mean of u on each sphere rS is dominated by that of U, which is the harmonic function with boundary values 1 on the right hemisphere and −1 on the left one.

Holomorphically embedded discs with rapidly growing area

1999 ◽  
Vol 129 (2) ◽  
pp. 343-349
Author(s):  
Josip Globevnik
Keyword(s):  
Unit Ball ◽  
Open Unit ◽  
Open Unit Ball

It is shown that if V is a closed submanifold of the open unit ball of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ 1. It is also shown that if V is a closed submanifold of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ ∞.

scholarly journals Homogeneously Polyanalytic Kernels on the Unit Ball and the Siegel Domain

2021 ◽  
Vol 15 (6) ◽  
Author(s):  
Christian Rene Leal-Pacheco ◽  
Egor A. Maximenko ◽  
Gerardo Ramos-Vazquez
Keyword(s):  
Unit Ball ◽  
Siegel Domain
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