Let $H(\mathbb{D})$ be the space of all analytic functions on $\mathbb{D}$, $u,v\in H(\mathbb{D})$ and $\varphi,\psi$ be self-map $(\varphi,\psi:\mathbb{D}\rightarrow \mathbb{D})$. Difference of weighted composition operator is denoted by $uC_\varphi -vC_\psi$ and defined as follows \begin{align*} (uC_\varphi -vC_\psi)f(z) = u(z) f{(\varphi(z))}- v(z) f(\psi(z)) ,\quad f\in H(\mathbb{D} ), \quad z\in \mathbb{D}. \end{align*} In this paper, boundedness of difference of weighted composition operator from Cauchy transform into Dirichlet space will be considered and an equivalence condition for boundedness of such operator will be given. Then the norm of composition operator between the mentioned spaces will be studied and it will be shown that $\|C_\varphi\|\geq 1$ and there is no composition isometry from Cauchy transform into Dirichlet space.
Abbasi, E. (2024). Difference of weighted composition operator from Cauchy transform space into Dirichlet space. Journal of Advanced Mathematical Modeling, 14(2), 87-95. doi: 10.22055/jamm.2024.46438.2270
MLA
Abbasi, E. . "Difference of weighted composition operator from Cauchy transform space into Dirichlet space", Journal of Advanced Mathematical Modeling, 14, 2, 2024, 87-95. doi: 10.22055/jamm.2024.46438.2270
HARVARD
Abbasi, E. (2024). 'Difference of weighted composition operator from Cauchy transform space into Dirichlet space', Journal of Advanced Mathematical Modeling, 14(2), pp. 87-95. doi: 10.22055/jamm.2024.46438.2270
CHICAGO
E. Abbasi, "Difference of weighted composition operator from Cauchy transform space into Dirichlet space," Journal of Advanced Mathematical Modeling, 14 2 (2024): 87-95, doi: 10.22055/jamm.2024.46438.2270
VANCOUVER
Abbasi, E. Difference of weighted composition operator from Cauchy transform space into Dirichlet space. Journal of Advanced Mathematical Modeling, 2024; 14(2): 87-95. doi: 10.22055/jamm.2024.46438.2270
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