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On Properties of Hilbert Transform of Finite Complex Measures

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Abstract

In the present paper we study asymptotic behavior of the distribution function of the Hilbert transform of the finite complex measure and using the notion of \({Q}^{\prime }\)-integration introduced by Titchmarsh we prove that the Hilbert transform of the finite complex measure \({Q}^{\prime }\)-integrable on the real axis R, and the \({Q}^{\prime }\)-integral of this function equals to zero.

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Authors and Affiliations

  1. Baku State University, Baku, AZ, 1148, Azerbaijan

    Rashid A. Aliev

  2. Institute of Mathematics and Mechanics, NAS of Azerbaijan, Baku, AZ, 1141, Azerbaijan

    Rashid A. Aliev

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  1. Rashid A. Aliev
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Correspondence to Rashid A. Aliev.

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Communicated by Vladimir Bolotnikov.

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Aliev, R.A. On Properties of Hilbert Transform of Finite Complex Measures. Complex Anal. Oper. Theory 10, 171–185 (2016). https://doi.org/10.1007/s11785-015-0480-9

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  • DOI: https://doi.org/10.1007/s11785-015-0480-9

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