## Rocky Mountain Journal of Mathematics

### On a logarithmic Hardy-Bloch type space

#### Abstract

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 $f\in BH_{p,L}$.

#### Article information

Source
Rocky Mountain J. Math., Volume 44, Number 5 (2014), 1669-1683.

Dates
First available in Project Euclid: 1 January 2015

https://projecteuclid.org/euclid.rmjm/1420071561

Digital Object Identifier
doi:10.1216/RMJ-2014-44-5-1669

Mathematical Reviews number (MathSciNet)
MR3295649

Zentralblatt MATH identifier
1303.30048

Subjects
Primary: 30H10: Hardy spaces 30H30: Bloch spaces 30H35: BMO-spaces

#### Citation

Wu, Xiaoming; Ye, Shanli. On a logarithmic Hardy-Bloch type space. Rocky Mountain J. Math. 44 (2014), no. 5, 1669--1683. doi:10.1216/RMJ-2014-44-5-1669. https://projecteuclid.org/euclid.rmjm/1420071561

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