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Riesz-Fejér Inequalities for Harmonic Functions

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Abstract

In this article, we prove the Riesz - Fejér inequality for complex-valued harmonic functions in the harmonic Hardy space hp for all p > 1. The result is sharp for p ∈ (1,2]. Moreover, we prove two variant forms of Riesz-Fejér inequality for harmonic functions, for the special case p = 2.

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Acknowledgements

The research of the first author was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project No. 1.12878.2018/12.1, and the work of the second author is supported by Mathematical Research Impact Centric Support (MATRICS) grant, File No.: MTR/2017/000367, by the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India. The third author initiated this work when he was a NBHM Postdoctoral Fellow at the Indian Statistical Institute Chennai Centre.

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Authors and Affiliations

  1. Kazan Federal University, Kremlevskaya 18, 420 008, Kazan, Russia

    Ilgiz R. Kayumov

  2. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600 036, India

    Saminathan Ponnusamy

  3. Indian Institute of Technology Ropar, Nangal Road, Rupnagar, Punjab, 140001, India

    Anbareeswaran Sairam Kaliraj

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  1. Ilgiz R. Kayumov
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  2. Saminathan Ponnusamy
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  3. Anbareeswaran Sairam Kaliraj
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Correspondence to Ilgiz R. Kayumov.

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Kayumov, I.R., Ponnusamy, S. & Kaliraj, A.S. Riesz-Fejér Inequalities for Harmonic Functions. Potential Anal 52, 105–113 (2020). https://doi.org/10.1007/s11118-018-9732-4

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  • DOI: https://doi.org/10.1007/s11118-018-9732-4

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