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Conditional Carleson Measures and Related Operators on Bergman Spaces

Abstract

In this paper, first we define generalized Carleson measure. Then we consider a special case of it, named conditional Carleson measure on the Bergman spaces. After that, we give a characterization of conditional Carleson measures on Bergman spaces. Moreover, by using this characterization we find an equivalent condition to boundedness of weighted conditional expectation operators on Bergman spaces.

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Correspondence to Y. Estaremi.

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Communicated by Farshid Abdollahi.

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Aliyan, A., Estaremi, Y. & Ebadian, A. Conditional Carleson Measures and Related Operators on Bergman Spaces. Bull. Iran. Math. Soc. 45, 997–1010 (2019). https://doi.org/10.1007/s41980-018-0180-0

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Keywords

  • Bergman space
  • Conditional expectation
  • Generalized Carleson measure
  • Conditional Carleson measure
  • Möbius transformation