Nonfactorization Theorems in Weighted Bergman and Hardy Spaces on the Unit Ball of C n (n > 1)

1983 ◽  
Vol 277 (1) ◽  
pp. 203 ◽  
Author(s):  
M. Seetharama Gowda
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Bergman And Hardy Spaces

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 The group of isometries on Hardy spaces of the n-ball and the polydisc

1980 ◽  
Vol 21 (2) ◽  
pp. 199-204 ◽  
Author(s):  
Earl Berkson ◽  
Horacio Porta
Keyword(s):  
Euclidean Space ◽  
Unit Ball ◽  
Complex Plane ◽  
Hardy Spaces ◽  
Inner Product ◽  
Euclidean Norm ◽  
Dimensional Euclidean Space ◽  
Open Unit ◽  
Open Unit Ball ◽  
Group Of Isometries

Let C be the complex plane, and U the disc |Z| < 1 in C. Cn denotes complex n-dimensional Euclidean space, <, > the inner product, and | · | the Euclidean norm in Cn;. Bn will be the open unit ball {z ∈ Cn:|z| < 1}, and Un will be the unit polydisc in Cn. For l ≤ p < ∞, p ≠ 2, Gp(Bn) (resp., Gp(Un)) will denote the group of all isometries of Hp(Bn) (resp., Hp(Un)) onto itself, where Hp(Bn) and HP(Un) are the usual Hardy spaces.

scholarly journals Independent inner functions in the classical domains

1987 ◽  
Vol 29 (2) ◽  
pp. 229-236
Author(s):  
Tomasz M. Wolniewicz
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Isometric Embedding ◽  
Symmetric Domain ◽  
Type I ◽  
Bounded Symmetric Domains ◽  
Inner Functions ◽  
Main Result Theorem ◽  
Complemented Subspace ◽  
Result Theorem

Let Bn denote the unit ball and Un the unit polydisc in Cn. In this paper we consider questions concerned with inner functions and embeddings of Hardy spaces over bounded symmetric domains. The main result (Theorem 2) states that for a classical symmetric domain D of type I and rank(D) = s, there exists an isometric embedding of Hl(Us) onto a complemented subspace of Hl(D). This should be compared with results of Wojtaszczyk [13] and Bourgain [3, 4] which state that H1(Bn) is isomorphic to Hl(U) while for n>m, Hl(Un) cannot be isomorphically embedded onto a complemented subspace of H1(Um). Since balls are the only bounded symmetric domains of rank 1 and they are of type I, Theorem 2 shows that if rank(D1) = 1, rank(D2) > 1 then H1(D1) is not isomorphic to H1(D2). It is natural to expect this to hold always when rank(D1 ≠ rank(D2) but unfortunately we were not able to prove this.

scholarly journals Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Sei-Ichiro Ueki ◽  
Luo Luo
Keyword(s):  
Unit Ball ◽  
Composition Operator ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Multiplication Operator ◽  
Essential Norm ◽  
Multiplication Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

We estimate the essential norm of a compact weighted composition operator acting between different Hardy spaces of the unit ball in . Also we will discuss a compact multiplication operator between Hardy spaces.

scholarly journals Norm of the Hilbert matrix on Bergman and Hardy spaces and a theorem of Nehari type

2008 ◽  
Vol 254 (11) ◽  
pp. 2800-2815 ◽  
Author(s):  
Milutin Dostanić ◽  
Miroljub Jevtić ◽  
Dragan Vukotić
Keyword(s):  
Hardy Spaces ◽  
Hilbert Matrix ◽  
Bergman And Hardy Spaces

scholarly journals Bounded and compact multipliers between Bergman and Hardy spaces

1999 ◽  
Vol 35 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Stephen M. Buckley ◽  
M. S. Ramanujan ◽  
Dragan Vukotić
Keyword(s):  
Hardy Spaces ◽  
Bergman And Hardy Spaces
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