Accessibility navigation


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

[img]
Preview
Text (Open Access) - Published Version
· Available under License Creative Commons Attribution.
· Please see our End User Agreement before downloading.

804kB
[img] Text - Accepted Version
· Restricted to Repository staff only

362kB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

Official URL: https://nyjm.albany.edu/j/2022/28-30.html

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
Refereed:Yes
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:104158
Publisher:State University of New York

Downloads

Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation