Boundedness of Toeplitz operators and division theorems in spaces H^p(ω)

Abstract

The article gives a complete description of those functions h ∈ L ¹(Tⁿ ), for which the Toeplitz operator T_h (f) is bounded in some weighted spaces H^p (ω) (1<p<+∞) of functions holomorphic in the unit polydisc Uⁿ of Cⁿ . Also, a theorem on division by good enough inner functions is established.

Keywords:

• Toeplitz operators
• Anisotropic spaces
• Polydisc
• Good-inner function
• Classification Numbers: 45P05
• 32A36

Acknowledgements

The author was supported by NFSAT MA070-02/CRDF 12011.