• 충청수학회지
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• 제24권3호
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• pp.533-541
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• 2011

Let ${\omega}$ be a normal function. In this paper, we will extend the concept of Bloch space to Bloch-type space related with normal function ${\omega}$. We will investigate the properties of Bloch-type space ${\mathcal{B}}_{\omega}$ and the little Bloch-type space ${\mathcal{B}}_{{\omega},0}$ with weight ${\omega}$.

• 대한수학회지
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• 제51권1호
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• pp.125-135
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• 2014

We study the compact intertwining relations for composition operators, whose intertwining operators are Volterra type operators from the weighted Bergman spaces to the weighted Bloch spaces in the unit disk. As consequences, we find a new connection between the weighted Bergman spaces and little weighted Bloch spaces through this relations.

• Korean Journal of Mathematics
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• 제26권1호
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• pp.87-101
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• 2018

The purpose of this paper is to define a new class of hyperholomorphic functions spaces, which will be called $F^{\alpha}_{{\omega},G}$(p, q, s) type spaces. For this class, we characterize hyperholomorphic weighted ${\alpha}$-Bloch functions by functions belonging to $F^{\alpha}_{{\omega},G}$(p, q, s) spaces under some mild conditions. Moreover, we give some essential properties for the extended weighted little ${\alpha}$-Bloch spaces. Also, we give the characterization for the hyperholomorphic weighted Bloch space by the integral norms of $F^{\alpha}_{{\omega},G}$(p, q, s) spaces of hyperholomorphic functions. Finally, we will give the relation between the hyperholomorphic ${\mathcal{B}}^{\alpha}_{{\omega},0}$ type spaces and the hyperholomorphic valued-functions space $F^{\alpha}_{{\omega},G}$(p, q, s).