Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar, Odisha
10.22034/kjm.2021.243561.1964
Abstract
Let $\psi\in L^{\infty}(\mathbb{U_{+}}),$ where $\mathbb{U_{+}}$ is the upper half plane in $\mathbb{C}$ and $S_{\psi}$ be the little Hankel operator with symbol $\psi$ defined on the Bergman space $L_{a}^{2}(\mathbb{U}_{+}).$ In this paper we have shown that if $S_{\psi}$ is of finite rank then $\psi=\varphi+\chi,$ where $\chi\in \left(\overline{L_{a}^{2}(\mathbb{U}_{+})}\right)^{\perp}\bigcap L^{\infty}(\mathbb{U}_{+})$ and $\overline{\varphi}$ is a linear combination of $d_{\overline{w}}, w\in \mathbb{U}_{+}$ and some of their derivatives.
Das, S., & Das, N. (2022). Finite rank little Hankel operators on $L_{a}^{2}(\mathbb{U}_{+})$. Khayyam Journal of Mathematics, 8(1), 25-32. doi: 10.22034/kjm.2021.243561.1964
MLA
Sworup Kumar Das; Namita Das. "Finite rank little Hankel operators on $L_{a}^{2}(\mathbb{U}_{+})$". Khayyam Journal of Mathematics, 8, 1, 2022, 25-32. doi: 10.22034/kjm.2021.243561.1964
HARVARD
Das, S., Das, N. (2022). 'Finite rank little Hankel operators on $L_{a}^{2}(\mathbb{U}_{+})$', Khayyam Journal of Mathematics, 8(1), pp. 25-32. doi: 10.22034/kjm.2021.243561.1964
VANCOUVER
Das, S., Das, N. Finite rank little Hankel operators on $L_{a}^{2}(\mathbb{U}_{+})$. Khayyam Journal of Mathematics, 2022; 8(1): 25-32. doi: 10.22034/kjm.2021.243561.1964