scholarly journals Möbius invariant Hilbert spaces of holomorphic functions in the unit ball of ${\bf C}\sp n$

1991 ◽  
Vol 323 (2) ◽  
pp. 823-842
Author(s):  
Ke He Zhu
Keyword(s):  
Unit Ball ◽  
Hilbert Spaces ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions

Holomorphic Functions with Positive Real Part

1982 ◽  
Vol 34 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Eric Sawyer
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Convex Cone ◽  
Holomorphic Functions ◽  
Positive Real Part ◽  
Positive Real ◽  
Spaces Of Holomorphic Functions ◽  
Extreme Element ◽  
Image Position ◽  
Special Case

The main purpose of this note is to prove a special case of the following conjecture.Conjecture. If F is holomorphic on the unit ball Bn in Cn and has positive real part, then F is in Hp(Bn) for 0 < p < ½(n + 1).Here Hp(Bn) (0 < p < ∞) denote the usual Hardy spaces of holomorphic functions on Bn. See below for definitions. We remark that the conjecture is known for 0 < p < 1 and that some evidence for it already exists in the literature; for example [1, Theorems 3.11 and 3.15] where it is shown that a particular extreme element of the convex cone of functionsis in Hp(B2) for 0 < p < 3/2.

scholarly journals Hilbert spaces of tensor-valued holomorphic functions on the unit ball of ℂn

2004 ◽  
Vol 214 (2) ◽  
pp. 303-322 ◽  
Author(s):  
Stephen Hwang ◽  
Yang Liu ◽  
Genkai Zhang
Keyword(s):  
Unit Ball ◽  
Hilbert Spaces ◽  
Holomorphic Functions
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