Boundedness of a new kind of Toeplitz operator on $2\pi$-periodic holomorphic functions on the upper halfplane

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, University of Kurdistan, Sanandaj, Iran

2 Department of mathematics, Faculty of Science, University of Kurdistan, Sanandaj, Iran

Abstract

In the present paper, We introduce a new kind of Toeplitz operators on the spaces of $2\pi$ periodic holomorphic functions on the upper halfplane equipped with an integral norm similar to the norm of $L^{p}$ spaces. We prove the boundedness of Toeplitz operators in the case of bounded symbols. Also, we state some open problems for unbounded symbols and other cases in which our spaces are not Hilbert spaces.

Keywords