International Journal of Nonlinear Analysis and Applications

On the action of Toeplits operators into new BMOA type spaces in the unit disk

Articles in Press

Document Type : Research Paper

Authors

1 Saratov National Research State University named after N. G. Chernyshevsky, Russia

2 Department of Higher Mathematics, St. Petersburg Mining University, Russia

10.22075/ijnaa.2024.33014.4917

Abstract

 We provide new sharp results on the action of Toeplitz operators from Triebel and Besov spaces to new BMOA-type function spaces on the unit disk.  In this paper, we consider $s\geq1$ case in previous papers $s<1$ was covered for $BMOA_{s,q}$ and $BMOA_s^p$ spaces. We modify a little our previously known proofs.

Keywords

[1] A.B. Aleksandrov, Function Theory in the Ball, in Several Complex Variables II, Springer-Verlag, New York, 1994.
[2] A.B. Aleksandrov and V.V. Peller, Hankel operators and similarity to a contraction, Int. Math. Res. Notices 6 (1996), 264–275.
[3] R. Fefferman, Bounded mean oscillation on the polydisk, Ann. Math. 110 (1979), no. 2, 395–406.
[4] A. Harutyunyan and F. Shamoyan, Toeplitz operators in multidimensional spaces Hp(α) of M.M. Djrbashian, J. Contemp. Math. An., Nat. Acad. Sci. Armenia 30 (1995), no. 2, 70–78.
[5] S. Janson, J. Petre, and S., Semmes, On the action of Hankel and Toeplitz operators on some function spaces, Duke. Math. J. 51 (1984), no. 4, 937–957.
[6] J. Ortega and J. Fabrega, Holomorphic Triebel-Lizorkin spaces, J. Funct. Anal. 151 (1997), no. 1, 177–212.
[7] J. Ortega and J. Fabrega, Pointwise multipliers and corona type decomposition in BMOA, Ann. Inst. Fourier 46 (1996), no. 1, 111–137.
[8] R.F. Shamoyan, Multipliers, Toeplitz operators and duality in some spaces of analytic functions in the unit polydisk, PhD Dissertation, Moscow, 2001.
[9] R.F. Shamoyan, On multipliers from Bergman-type spaces to Hardy spaces in the polydisk, Ukrain. Math. J. 10 (2000), 1405–1415.
[10] R.F. Shamoyan, Generalized Hardy transformation and Toeplits operators in BMOA-type function spaces in the unit disk, Ukrain. Math. J. 53 (2001), 1260–1274.
[11] R.F. Shamoyan and M. Arsenovic, On multipliers on holomorphic Fp,q α type spaces on the unit polydisc, J. Siber. Federal Univ. Math. Phys. 5 (2012), no. 4, 471–479.
[12] R.F. Shamoyan, A.N. Shipka, On some new projection theorems and sharp estimates in Herz type spaces in bounded pseudoconvex domains, Vestnik KRAUNC. Phis.-Math. Nauki 21 (2018), no. 1, 64—77.
[13] R.F. Shamoyan and E.B. Tomashevskaya, On new sharp theorems for multifunctional BMOA type spaces in bounded pseudoconvex domains, Vestnik KRAUNC. Phis.-Math. 32 (2020), no. 3, 102-–113.
International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 20 June 2024
  • Receive Date: 18 January 2024
  • Accept Date: 16 March 2024