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Conditional Carleson Measures and Related Operators on Bergman Spaces

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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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Authors and Affiliations

  1. Department of Mathematics, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran

    A. Aliyan & Y. Estaremi

  2. Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran

    A. Ebadian

Authors
  1. A. Aliyan
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  2. Y. Estaremi
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  3. A. Ebadian
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Corresponding author

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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  • DOI: https://doi.org/10.1007/s41980-018-0180-0

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