Journal ArticleDOI
An integral operator on $H\sp p$
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In this paper, it was shown that Tg is bounded on Hp, 1 ≤ p < ∞ it and compact if and only if g ∊ BMOA and compact on VOMA.Abstract:
Let g be an analytic function on the unit disk D . We study the operator on the Hardy spaces Hp . We show that Tg is bounded on Hp , 1 ≤ p < ∞ it and only if g ∊ BMOA and compact if and only if g ∊ VOMA. Further on the Hilbert space H2 Tg is in the Schattcn ρ-class it and only if g is in the Besov space Bp , 1 < p < ∞. A relation of Tg with integration operators is also discussed.read more
Citations
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Journal ArticleDOI
Integration operators on Bergman spaces
TL;DR: In this article, the authors considered conditions on a positive integrable function such that the operator T_g$ is bounded on a Banach space of analytic functions, and showed that the condition is necessary and sufficient.
Journal ArticleDOI
An integral operator on $Hsp p$ and Hardy's inequality.
Alexandru Aleman,Joseph A. Cima +1 more
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Extended Cesàro operators on mixed norm spaces
TL;DR: In this paper, an extended Cesaro operator Tg with holomorphic symbol g in the unit ball B of C n was defined, where R g (z) = Σ n j=1 z j ∂ f /∂ zj is the radial derivative of g.
Journal ArticleDOI
On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball
TL;DR: In this article, an integral-type operator on the space H (B ) of all holomorphic functions on the unit ball B ⊂ C n P φ g ( f ) ( z ) = ∫ 0 1 f ( φ ( t z ) ) g ( t t, z ∈ B, where g ∈ H ( B ), g ( 0 ) = 0 and φ is a holomorphic self-map of B.
Book
Weighted Bergman Spaces Induced by Rapidly Increasing Weights
José Ángel Peláez,Jouni Rättyä +1 more
TL;DR: In this paper, the authors studied the weighted Bergman space of the unit disc and showed that it lies between the Hardy space $H^p$ and every classical weighted Bergmen space $A^p_\omega$ and that several finer function-theoretic properties of these spaces do not carry over to the more general Bergman spaces.
References
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Book
Bounded Analytic Functions
TL;DR: In this article, the Corona construction was used to construct Douglas algebra and interpolating sequences and Maximal Ideals were used to solve a set of problems in the Corona Construction.
Book
Operator theory in function spaces
TL;DR: In this article, the authors introduce the concept of bounded linear operators on the Bergman space and define a set of operators based on the bounded linear operator on the Hardy space, including the following operators:
Journal ArticleDOI
Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation
Journal ArticleDOI
On Analytic Functions of Bounded Mean Oscillation
Walter K. Hayman,Ch. Pommerenke +1 more
Journal ArticleDOI
Trace ideal criteria for Toeplitz operators
TL;DR: For a complex measure μ on the open unit disk U define an operator Tμ on a Hilbert space H of analytic functions with reproducing kernel k(z, w) by u.