Open Access
2014 On a logarithmic Hardy-Bloch type space
Xiaoming Wu, Shanli Ye
Rocky Mountain J. Math. 44(5): 1669-1683 (2014). DOI: 10.1216/RMJ-2014-44-5-1669


In this paper, given $0\lt p\lt \infty$, we define a logarithmic Hardy-Bloch type space \begin{multline*} BH_{p,L}=\left\{f(z)\in H(D):||f||_{p,L}\right.\\ \left.=\sup_{z\in D}(1-|z|)\log\frac{e}{1-|z|} M_p(|z|,f')\lt \infty\right\}. \end{multline*} Then we mainly study the relation between $BH_{p,L}$ and three classical spaces: Hardy space, Dirichlet type space and VMOA. We also obtain some estimates on the growth of $f\in BH_{p,L}$.


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Xiaoming Wu. Shanli Ye. "On a logarithmic Hardy-Bloch type space." Rocky Mountain J. Math. 44 (5) 1669 - 1683, 2014.


Published: 2014
First available in Project Euclid: 1 January 2015

zbMATH: 1303.30048
MathSciNet: MR3295649
Digital Object Identifier: 10.1216/RMJ-2014-44-5-1669

Primary: 30H10 , 30H30 , 30H35

Keywords: Bloch space , Dirichlet type space , Hardy space

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.44 • No. 5 • 2014
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