Mübariz Tapdıgoğlu GARAYEV, Mehmet GÜRDAL

Remarks on the zero Toeplitz product problem in the Bergman and Hardy spaces

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

In this article, we are interested in the zero Toeplitz product problem: for two symbols $f,g\in L^{\infty}\left( \mathbb{D},dA\right) ,$\ if the product $T_{f}T_{g}$\ is identically zero on $L_{a}^{2}\left( \mathbb{D}\right), $\ 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}\left( \mathbb{D}% \right) $ is also given.

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