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Boundedness of Projection Operator in Generalized Holomorphic and Harmonic Spaces of Functions of Hölder Type

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Modern Methods in Operator Theory and Harmonic Analysis (OTHA 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 291))

Abstract

We prove boundedness of holomorphic projection in the generalized Hölder type space of holomorphic functions in the unit disc with prescribed modulus of continuity and in the variable exponent generalized Hölder spaces of holomorphic functions in the unit disc. We also prove boundedness of harmonic projection in analogous spaces of harmonic functions.

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Acknowledgements

Alexey Karapetyants acknowledges the support of the Fulbright Research Scholarship program and the warm hospitality of the Mathematics Department at the State University of New York at Albany during the time when this research was completed. Alexey Karapetyants is partially supported by the Russian Foundation for Fundamental Research (Grant Number 18-01-00094).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, SUNY, Albany, NY, 12222, USA

    Alexey Karapetyants

  2. Department of Mathematics and Regional Mathematical Center, Southern Federal University, Rostov-on-Don, 344090, Russia

    Alexey Karapetyants

  3. Regional Mathematical Center, Southern Federal University, Rostov-on-Don, 344090, Russia

    Joel E. Restrepo

Authors
  1. Alexey Karapetyants
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  2. Joel E. Restrepo
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Correspondence to Joel E. Restrepo .

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Editors and Affiliations

  1. Institute of Mathematics, Mechanic and Computer Sciences and Regional Mathematical Center, Southern Federal University, Rostov-on-Don, Russia

    Alexey Karapetyants

  2. Department of Mathematics, Cinvestav, Santiago de Querétaro, Querétaro, Mexico

    Vladislav Kravchenko

  3. Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel

    Elijah Liflyand

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Karapetyants, A., Restrepo, J.E. (2019). Boundedness of Projection Operator in Generalized Holomorphic and Harmonic Spaces of Functions of Hölder Type. In: Karapetyants, A., Kravchenko, V., Liflyand, E. (eds) Modern Methods in Operator Theory and Harmonic Analysis. OTHA 2018. Springer Proceedings in Mathematics & Statistics, vol 291. Springer, Cham. https://doi.org/10.1007/978-3-030-26748-3_4

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