Geodesic
Products of Toeplitz operators on the Bergman spaces~$A_\alpha^2$
Algebra i analiz, Tome 18 (2006) no. 1, pp. 144-161.

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We give a sufficient and a necessary condition for the product of Toeplitz operators $T^\alpha_fT^\alpha_{\bar g}$, with $f$, $g$ analytic, to be bounded on the weighted Bergman space $L^2_a(\mathbb D,(1-|z|^2)^\alpha dA)$. We also show that the only compact product of weighted Toeplitz operators is the trivial one.
Keywords: weighted Bergman spaces, Toeplitz operators, reproducing kernel thesis. 
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S. Pott; E. Strouse. Products of Toeplitz operators on the Bergman spaces~$A_\alpha^2$. Algebra i analiz, Tome 18 (2006) no. 1, pp. 144-161. http://geodesic.mathdoc.fr/item/AA_2006_18_1_a5/

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