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Ardalani, Mohammad, Haftbaradaran, Saeed. (1400). Boundedness of a new kind of Toeplitz operator on $2\pi$-periodic holomorphic functions on the upper halfplane. هنرهای کاربردی, 13(1), 2665-2670. doi: 10.22075/ijnaa.2021.22314.2349
Mohammad Ali Ardalani; Saeed Haftbaradaran. "Boundedness of a new kind of Toeplitz operator on $2\pi$-periodic holomorphic functions on the upper halfplane". هنرهای کاربردی, 13, 1, 1400, 2665-2670. doi: 10.22075/ijnaa.2021.22314.2349
Ardalani, Mohammad, Haftbaradaran, Saeed. (1400). 'Boundedness of a new kind of Toeplitz operator on $2\pi$-periodic holomorphic functions on the upper halfplane', هنرهای کاربردی, 13(1), pp. 2665-2670. doi: 10.22075/ijnaa.2021.22314.2349
Ardalani, Mohammad, Haftbaradaran, Saeed. Boundedness of a new kind of Toeplitz operator on $2\pi$-periodic holomorphic functions on the upper halfplane. هنرهای کاربردی, 1400; 13(1): 2665-2670. doi: 10.22075/ijnaa.2021.22314.2349

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

International Journal of Nonlinear Analysis and Applications
مقاله 217، دوره 13، شماره 1، خرداد 2022، صفحه 2665-2670    اصل مقاله (359.75 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22314.2349
نویسندگان
Mohammad Ali Ardalani* 1؛ Saeed Haftbaradaran2
1Department of Mathematics, Faculty of Science, University of Kurdistan, Sanandaj, Iran
2Department of mathematics, Faculty of Science, University of Kurdistan, Sanandaj, Iran
تاریخ دریافت: 16 دی 1399،  تاریخ پذیرش: 01 اسفند 1399 
چکیده
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.
کلیدواژه‌ها
Toeplitz operator؛ projection؛ $2\pi$ periodic holomorphic functions؛ upper halfplane
مراجع

[1] M.A. Ardalani, On the isomorphism classification of spaces 2π periodic holomorphic functions on the upper halfplane, J. Math. Anal. Appl. 459 (2018) 350–359.

[2] O. Constantin and J. A. Pelaez, Boudndedness of the Bergman projection on Lp-spaces with expotential weights, Bull. Sci. Math. 139 (2015) 245–268.

[3] M. Dostanic, Unboundedness of the Bergman projection on Lp spaces with expotential weights, Proc. Edinb. Math. Soc. 47 (2004) 111–117.

[4] M. Englis, Toeplitz operators and weighted Bergman kernels, J. Funct. Anal. 255 (6) (2008) 1419–1457.

[5] S. Grudsky, A. Karapetyants, N. Vasilevski, Toeplitz operators on the unit ball of CN with radial symbols, J. Oper. Theory 49 (2003) 325–346.

[6] W. Lusky and J. Taskinen, Toeplitz operators on Bergman spaces and Hardy multipliers, Studia. Math. 204 (2011) 137–154.

[7] K. Zhu, Operator Theory in Function Spaces. 2nd edition, Mathematical surves and monographs, Vol. 138, American Mathematical Society, Providence, RI, 2007.

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