Details

Autor(en) / Beteiligte

• DONG, XING-TANG
• LIU, CONGWEN
• ZHOU, ZE-HUA

Titel

QUASIHOMOGENEOUS TOEPLITZ OPERATORS WITH INTEGRABLE SYMBOLS ON THE HARMONIC BERGMAN SPACE

Ist Teil von

• Bulletin of the Australian Mathematical Society, 2014-12, Vol.90 (3), p.494-503

Ort / Verlag

Cambridge, UK: Cambridge University Press

Erscheinungsjahr

2014

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we completely determine the commutativity of two Toeplitz operators on the harmonic Bergman space with integrable quasihomogeneous symbols, one of which is of the form $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}e^{ik\theta }r^{\, {m}}$. As an application, the problem of when their product is again a Toeplitz operator is solved. In particular, Toeplitz operators with bounded symbols on the harmonic Bergman space commute with $T_{e^{ik\theta }r^{\, {m}}}$ only in trivial cases, which appears quite different from results on analytic Bergman space in Čučković and Rao [‘Mellin transform, monomial symbols, and commuting Toeplitz operators’, J. Funct. Anal.154 (1998), 195–214].