Weak BMO and Toeplitz operators on Bergman spacesTaskinen, 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
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/SummaryInspired 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.
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