Hankel operators on the Bergman space

2007 ◽  
pp. 207-252
Author(s):  
Kehe Zhu
Keyword(s):  
Bergman Space ◽  
Hankel Operators

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.

Middle Hankel Operators on Bergman Space

2020 ◽  
pp. 325-336
Author(s):  
Lizhong Peng ◽  
Genkai Zhang
Keyword(s):  
Bergman Space ◽  
Hankel Operators

scholarly journals Hankel operators induced by radial Bekollé–Bonami weights on Bergman spaces

2019 ◽  
Vol 296 (1-2) ◽  
pp. 211-238 ◽  
Author(s):  
José Ángel Peláez ◽  
Antti Perälä ◽  
Jouni Rättyä
Keyword(s):  
Bergman Space ◽  
Bergman Spaces ◽  
Hankel Operators ◽  
Weighted Bergman Space ◽  
Doubling Condition ◽  
Weighted Mean ◽  
Mean Oscillation ◽  
Radial Weight ◽  
Classical Setting

Abstract We study big Hankel operators $$H_f^\nu :A^p_\omega \rightarrow L^q_\nu $$ H f ν : A ω p → L ν q generated by radial Bekollé–Bonami weights $$\nu $$ ν , when $$1<p\le q<\infty $$ 1 < p ≤ q < ∞ . Here the radial weight $$\omega $$ ω is assumed to satisfy a two-sided doubling condition, and $$A^p_\omega $$ A ω p denotes the corresponding weighted Bergman space. A characterization for simultaneous boundedness of $$H_f^\nu $$ H f ν and $$H_{{\overline{f}}}^\nu $$ H f ¯ ν is provided in terms of a general weighted mean oscillation. Compared to the case of standard weights that was recently obtained by Pau et al. (Indiana Univ Math J 65(5):1639–1673, 2016), the respective spaces depend on the weights $$\omega $$ ω and $$\nu $$ ν in an essentially stronger sense. This makes our analysis deviate from the blueprint of this more classical setting. As a consequence of our main result, we also study the case of anti-analytic symbols.

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