Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213120220301Boundedness of a new kind of Toeplitz operator on $2\pi$-periodic holomorphic functions on the upper halfplane26652670598810.22075/ijnaa.2021.22314.2349ENMohammad AliArdalaniDepartment of Mathematics, Faculty of Science, University of Kurdistan, Sanandaj, Iran0000-0002-3214-3116Saeed HaftbaradaranDepartment of mathematics, Faculty of Science, University of Kurdistan, Sanandaj, IranJournal Article20210105In 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.https://ijnaa.semnan.ac.ir/article_5988_b276decd766b7345496d6cf8aefd7528.pdf