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Keywords:

  • Toeplitz operator;
  • Schatten-Herz class;
  • harmonic Bergman space MSC (2010) 47B35;
  • 32A37

Abstract

On the setting of the bounded domain Ω in equation image with C boundary, we introduce the Schatten-Herz classes Toeplitz operators. And in term of averaging functions and Berezin transforms, we characterize those finite positive Borel measures μ on Ω for which the induced Toeplitz operators are in Shatten-Herz classes. As some preliminary results, we obtain the sharp estimate of integral means for the harmonic Bergman kernel on the level surface and the boundedness of the Berezin transform on the Herz spaces.