scholarly journals Study on Properties of Big Hankel Operator on Harmonic Bergman Space

2018 ◽  
Vol 08 (03) ◽  
pp. 203-207
Author(s):  
静 杨
Keyword(s):  
Bergman Space ◽  
Hankel Operator ◽  
Harmonic Bergman Space

Interpolating sequences for the derivatives of Bloch functions

1992 ◽  
Vol 34 (1) ◽  
pp. 35-41 ◽  
Author(s):  
K. R. M. Attele
Keyword(s):  
Bergman Space ◽  
Hankel Operator ◽  
Essential Norm ◽  
Bloch Function ◽  
Sufficient Condition ◽  
Bloch Functions ◽  
Interpolating Sequences ◽  
Analytic Symbol ◽  
Derivatives Of

AbstractWe prove that sufficiently separated sequences are interpolating sequences for f′(z)(1−|z|2) where f is a Bloch function. If the sequence {zn} is an η net then the boundedness f′(z)(1−|z|2) on {zn} is a sufficient condition for f to be a Bloch function. The essential norm of a Hankel operator with a conjugate analytic symbol acting on the Bergman space is shown to be equivalent to .

scholarly journals Finite-rank intermediate Hankel operators on the Bergman space

2001 ◽  
Vol 25 (1) ◽  
pp. 19-31 ◽  
Author(s):  
Takahiko Nakazi ◽  
Tomoko Osawa
Keyword(s):  
Bergman Space ◽  
Orthogonal Projection ◽  
Finite Rank ◽  
Lebesgue Space ◽  
Unit Disc ◽  
Hankel Operator ◽  
Hankel Operators ◽  
Weighted Bergman Space ◽  
Open Unit ◽  
Open Unit Disc

LetL2=L2(D,r dr dθ/π)be the Lebesgue space on the open unit disc and letLa2=L2∩ℋol(D)be the Bergman space. LetPbe the orthogonal projection ofL2ontoLa2and letQbe the orthogonal projection ontoL¯a,02={g∈L2;g¯∈La2,   g(0)=0}. ThenI−P≥Q. The big Hankel operator and the small Hankel operator onLa2are defined as: forϕinL∞,Hϕbig(f)=(I−P)(ϕf)andHϕsmall(f)=Q(ϕf)(f∈La2). In this paper, the finite-rank intermediate Hankel operators betweenHϕbigandHϕsmallare studied. We are working on the more general space, that is, the weighted Bergman space.

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