Abstract
In this article, we are interested in the zero Toeplitz product problem: for two symbols f, g is an element of L-infinity (D, dA), if the product TfTg is identically zero on L-a(2)(D), then can we claim T-f or T-g is identically zero? We give a particular solution of this problem. A new proof of one particular case of the zero Toeplitz product problem in the Hardy space H-2 (D) is also given.