<p>We investigate little Hankel operators on logarithmic Bloch type spaces. In 2003, Ohno, Stroethoff and Zhao give a necessary and sufficient condition for weighted composition operators on Bloch type spaces to be bounded. Bonami and Luo characterize the boundedness of little Hankel operator with anti-holomorphic symbols between Bergman spaces. Based on these results, the authors have previously given a necessary and sufficient condition for little Hankel operators with anti-holomorphic symbols on Bloch type spaces to be bounded. In this paper, we consider this condition on logarithmic Bloch type spaces. The boundedness of weighted composition operators on these spaces are investigated by Stević and Agarwal. In order to show a characterization for bounded little Hankel operators, we apply logarithmic Forelli-Rudin type estimates which are obtained by Chen and Zhang. These estimates give us a necessary and sufficient condition for little Hankel operator with anti-holomorphic symbol on logarithmic Bloch type spaces to be bounded.</p>

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Little Hankel operators on logarithmic Bloch type spaces

  • Kiyoki Tanaka,
  • Satoshi Yamaji

摘要

We investigate little Hankel operators on logarithmic Bloch type spaces. In 2003, Ohno, Stroethoff and Zhao give a necessary and sufficient condition for weighted composition operators on Bloch type spaces to be bounded. Bonami and Luo characterize the boundedness of little Hankel operator with anti-holomorphic symbols between Bergman spaces. Based on these results, the authors have previously given a necessary and sufficient condition for little Hankel operators with anti-holomorphic symbols on Bloch type spaces to be bounded. In this paper, we consider this condition on logarithmic Bloch type spaces. The boundedness of weighted composition operators on these spaces are investigated by Stević and Agarwal. In order to show a characterization for bounded little Hankel operators, we apply logarithmic Forelli-Rudin type estimates which are obtained by Chen and Zhang. These estimates give us a necessary and sufficient condition for little Hankel operator with anti-holomorphic symbol on logarithmic Bloch type spaces to be bounded.