@article { author = {Das, Sworup and Das, Namita}, title = {Finite rank little Hankel operators on $L_{a}^{2}(\mathbb{U}_{+})$}, journal = {Khayyam Journal of Mathematics}, volume = {8}, number = {1}, pages = {25-32}, year = {2022}, publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)}, issn = {2423-4788}, eissn = {2423-4788}, doi = {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.}, keywords = {Bergman space,Upper half plane,little Hankel operators,finite rank operators,Essentially bounded functions}, url = {https://www.kjm-math.org/article_138709.html}, eprint = {https://www.kjm-math.org/article_138709_a728a1cba0e0e1d6555daf0ecf8dfd7f.pdf} }