Real, complex and functional analysis

Toeplitz operators in Sobolev spaces of analytic functions and applications

F. A. Shamoyan, V. A. Bednazh

Bryansk State University, Bezhitskaya Str., 14, 241036, Bryansk, Russia

Abstract: A complete description of the integrable functions $ h $ on the unit circle, for which the Toeplitz operator with symbol $ h $ is a bounded operator in weighted spaces of Sobolev type of analytic functions in a disc. An application is also installed results in matters of the factorization of analytic functions.

Keywords: Teoplitz operator, inner functions, linear functional, unit disc.

UDC: 517.53

MSC: 30J05,30J10

Received June 26, 2016, published March 6, 2017

DOI: 10.17377/semi.2017.14.017