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  1. Integral Equations and Operator Theory
  2. Integral Equations and Operator Theory : Volume 61
  3. Integral Equations and Operator Theory : Volume 61, Issue 4, August 2008
  4. Carleson Measures for the Bloch Space
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Integral Equations and Operator Theory : Volume 88
Integral Equations and Operator Theory : Volume 87
Integral Equations and Operator Theory : Volume 86
Integral Equations and Operator Theory : Volume 85
Integral Equations and Operator Theory : Volume 84
Integral Equations and Operator Theory : Volume 83
Integral Equations and Operator Theory : Volume 82
Integral Equations and Operator Theory : Volume 81
Integral Equations and Operator Theory : Volume 80
Integral Equations and Operator Theory : Volume 79
Integral Equations and Operator Theory : Volume 78
Integral Equations and Operator Theory : Volume 77
Integral Equations and Operator Theory : Volume 76
Integral Equations and Operator Theory : Volume 75
Integral Equations and Operator Theory : Volume 74
Integral Equations and Operator Theory : Volume 73
Integral Equations and Operator Theory : Volume 72
Integral Equations and Operator Theory : Volume 71
Integral Equations and Operator Theory : Volume 70
Integral Equations and Operator Theory : Volume 69
Integral Equations and Operator Theory : Volume 68
Integral Equations and Operator Theory : Volume 67
Integral Equations and Operator Theory : Volume 66
Integral Equations and Operator Theory : Volume 65
Integral Equations and Operator Theory : Volume 64
Integral Equations and Operator Theory : Volume 63
Integral Equations and Operator Theory : Volume 62
Integral Equations and Operator Theory : Volume 61
Integral Equations and Operator Theory : Volume 61, Issue 4, August 2008
Sharp Two Weight Inequalities for Commutators of Riemann-Liouville and Weyl Fractional Integral Operators
Boundedness of Commutators of Marcinkiewicz Integral with Rough Variable Kernel
Convolution-Dominated Operators on Discrete Groups
Carleson Measures for the Bloch Space
Conditions Implying Self-adjointness of Operators
Seminorm Related to Banach-Saks Property and Real Interpolation of Operators
Hankel and Toeplitz Transforms on H 1: Continuity, Compactness and Fredholm Properties
On the Cowen-Douglas Class for Banach Space Operators
Integral Equations and Operator Theory : Volume 61, Issue 3, July 2008
Integral Equations and Operator Theory : Volume 61, Issue 2, June 2008
Integral Equations and Operator Theory : Volume 61, Issue 1, May 2008
Integral Equations and Operator Theory : Volume 60
Integral Equations and Operator Theory : Volume 59
Integral Equations and Operator Theory : Volume 58
Integral Equations and Operator Theory : Volume 57
Integral Equations and Operator Theory : Volume 56
Integral Equations and Operator Theory : Volume 55
Integral Equations and Operator Theory : Volume 54
Integral Equations and Operator Theory : Volume 53
Integral Equations and Operator Theory : Volume 52
Integral Equations and Operator Theory : Volume 51
Integral Equations and Operator Theory : Volume 50
Integral Equations and Operator Theory : Volume 49
Integral Equations and Operator Theory : Volume 48
Integral Equations and Operator Theory : Volume 47
Integral Equations and Operator Theory : Volume 46
Integral Equations and Operator Theory : Volume 45
Integral Equations and Operator Theory : Volume 44
Integral Equations and Operator Theory : Volume 43
Integral Equations and Operator Theory : Volume 42
Integral Equations and Operator Theory : Volume 41
Integral Equations and Operator Theory : Volume 40
Integral Equations and Operator Theory : Volume 39
Integral Equations and Operator Theory : Volume 38
Integral Equations and Operator Theory : Volume 37
Integral Equations and Operator Theory : Volume 36
Integral Equations and Operator Theory : Volume 35
Integral Equations and Operator Theory : Volume 34
Integral Equations and Operator Theory : Volume 33
Integral Equations and Operator Theory : Volume 32
Integral Equations and Operator Theory : Volume 31
Integral Equations and Operator Theory : Volume 30
Integral Equations and Operator Theory : Volume 29
Integral Equations and Operator Theory : Volume 28
Integral Equations and Operator Theory : Volume 27

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Carleson Measures for the Bloch Space

Content Provider SpringerLink
Author Girela, Daniel Peláez, José Ángel Rättyä, Jouni Pérez González, Fernando
Copyright Year 2008
Abstract In this paper we study the positive Borel measures μ on the unit disc $${\mathbb{D}}$$ in $${\mathbb{C}}$$ for which the Bloch space $$\mathcal{B}$$ is continuously included in $$L^p(d\mu)$$ , 0 < p < ∞. We call such measures p-Bloch-Carleson measures. We give two conditions on a measure μ in terms of certain logarithmic integrals one of which is a necessary condition and the other a sufficient condition for μ being a p-Bloch-Carleson measure. We also give a complete characterization of the p-Bloch-Carleson measures within certain special classes of measures. It is also shown that, for p > 1, the p-Bloch-Carleson measures are exactly those for which the Toeplitz operator $$T_\mu$$ , defined by $$T_\mu(f)(z) = \int_\mathbb{D} {\frac {f(w)} {(1-\bar{w}z)^2}} d\mu(w) (f \epsilon L^1(d\mu), z \epsilon {\mathbb{D}})$$ , maps continuously $$L^{p\prime}\,(d\mu)$$ into the Bergman space A 1, $$\frac {1} {p}\,+\,\frac {1}{p\prime}\,=\,1$$ . Furthermore, we prove that if p > 1, α >-1 and ω is a weight which satisfies the Bekollé-Bonami $$\mathcal{B}_{p,\alpha}$$ -condition, then the measure $$\mu_{\alpha,p}$$ defined by $$d\mu_{\alpha,p}(z) = {(1-|z|^2)}^{\alpha}\omega(z)dA(z)$$ is a p-Bloch-Carleson-measure.We also consider the Banach space $$H^{\infty}_{\rm log}$$ of those functions f which are analytic in $${\mathbb{D}}$$ and satisfy $$|f(z)| = O\left({\rm log} \frac {1} {1-|z|}\right)$$ , as $$|z| \rightarrow 1$$ . The Bloch space is contained in $$H^{\infty}_{\rm log}$$ . We describe the p-Carleson measures for $$H^{\infty}_{\rm log}$$ and study weighted composition operators and a class of integration operators acting in this space. We determine which of these operators map $$H^{\infty}_{\rm log}$$ continuously to the weighted Bergman space $$A^{p}_{\alpha} (p > 0, \alpha > -1) $$ and show that they are automatically compact.
Ending Page 547
Page Count 37
Starting Page 511
File Format PDF
ISSN 0378620X
e-ISSN 14208989
Journal Integral Equations and Operator Theory
Issue Number 4
Volume Number 61
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2008-07-25
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword interpolating sequences Bloch functions, normal functions, normal families Bloch function weighted composition operators Analysis integration operators Bounded analytic functions Bergman spaces Carleson measures Bekollé-Bonami weights
Content Type Text
Resource Type Article
Subject Algebra and Number Theory Analysis
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