Journal of the Mathematical Society of Japan

On higher dimensional Luecking's theorem

Boo Rim CHOE

Full-text: Open access

Abstract

D. Luecking has recently proved that a Toeplitz operator with measure symbol on the Bergman space of unit disk has finite rank if and only if its symbols is a linear combination of point masses. In this note we extend this theorem to higher dimensional cases.

Article information

Source
J. Math. Soc. Japan, Volume 61, Number 1 (2009), 213-224.

Dates
First available in Project Euclid: 9 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1234189033

Digital Object Identifier
doi:10.2969/jmsj/06110213

Mathematical Reviews number (MathSciNet)
MR2272876

Zentralblatt MATH identifier
1162.47027

Subjects
Primary: 46E20: Hilbert spaces of continuous, differentiable or analytic functions 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 32A36: Bergman spaces

Keywords
Toeplitz operator Bergman space finite rank

Citation

CHOE, Boo Rim. On higher dimensional Luecking's theorem. J. Math. Soc. Japan 61 (2009), no. 1, 213--224. doi:10.2969/jmsj/06110213. https://projecteuclid.org/euclid.jmsj/1234189033


Export citation

References