Weak BMO and Toeplitz operators on Bergman spaces

Taskinen, J. and Virtanen, J. (2022) Weak BMO and Toeplitz operators on Bergman spaces. New York Journal of Mathematics, 28. pp. 773-790. ISSN 1076-9803

Abstract/Summary

Inspired by our previous work on the boundedness of Toeplitz operators, we introduce weak BMO and VMO type conditions, denoted by BWMO and VWMO, respectively, for functions on the open unit disc of the complex plane. We show that the average function of a function f ∈ BWMO is boundedly oscillating, and the analogous result holds for f ∈ VWMO. The result is applied for generalizations of known results on the essential spectra and norms of Toeplitz operators. Finally, we provide examples of functions satisfying the VWMO condition which are not in the classical VMO or even in BMO.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/104158
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	State University of New York
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