Abstract
Let $H(D)$ be an algebra of all holomorphic functions on the open unit disc $D$ and $X$ a subspace of $H(D)$. When $g$ is a function in $H(D)$, put $$ J_g(f)(z) = \int^z_0 f(\zeta)g^\prime(\zeta)d\zeta~{\rm and}~I_g(f)(z) = \int^z_0 f^\prime(\zeta)g(\zeta)d\zeta \quad (z \in D) $$ for $f$ in $X$. In this paper, we study $J[X] = \{g \in H(D)~;~J_g(f) \in X$ for all $f$ in $X \}$ and $I[X] = \{g \in H(D)~;~I_g(f) \in X$ for all $f$ in $X \}$. We apply the results to concrete spaces. For example, we study $J[X]$ and $I[X]$ when $X$ is a weighted Bloch space, a Hardy space or a Privalov space.
Citation
Takahiko Nakazi. "INTEGRAL OPERATORS ON A SUBSPACE OF HOLOMORPHIC FUNCTIONS ON THE DISC." Taiwanese J. Math. 12 (2) 389 - 400, 2008. https://doi.org/10.11650/twjm/1500574162
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