On generalized Toeplitz and little Hankel operators on Bergman spaces

Taskinen, J. and Virtanen, J. (2018) On generalized Toeplitz and little Hankel operators on Bergman spaces. Archiv der Mathematik, 110 (2). pp. 155-166. ISSN 1420-8938

 Preview
Text - Accepted Version

335kB

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

To link to this item DOI: 10.1007/s00013-017-1124-2

Abstract/Summary

We find a concrete integral formula for the class of generalized Toeplitz operators $T_a$ in Bergman spaces $A^p$, $1<p<\infty$, studied in an earlier work by the authors. The result is extended to little Hankel operators. We give an example of an $L^2$-symbol $a$ such that $T_{|a|}$ fails to be bounded in $A^2$, although $T_a : A^2 \to A^2$ is seen to be bounded by using the generalized definition. We also confirm that the generalized definition coincides with the classical Tone whenever the latter makes sense.

Item Type: Article Yes Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics 73602 Springer