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Authors: TATSUHIRO HONDA.
DOI: 10.24193/subbmath. 2022.2.08
Published Online: 2022-06-10
Published Print: 2022-06-30
pp. 317-328
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Abstract: Let $B_X$ be a bounded symmetric domain realized as the open unit ball of a JB*-triple $X$ which may be infinite dimensional. In this paper, we characterize the bounded weighted composition operators from the Hardy space $H^{infty}(mathbb{B}_X)$ into the $alpha $-Bloch space $mathcal{B}^alpha (B_X)$ on $mathbb{B}_X$. Later, we show the multiplication operator from $H^{infty}(mathbb{B}_X)$ into $mathcal{B}^alpha (B_X)$ is bounded. Also, we give the operator norm of the bounded multiplication operator.
Key words: α-Bloch space, weighted composition operator, bounded symmetric domain, JB*-triple.
Mathematics Subject Classification (2010): 32A18, 32M15.
