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Modified Fractional Hardy and Hardy-Littlewood Operators and Their Commutators

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Abstract

For modified fractional Hardy and Hardy-Littlewood operators and their commutators with symbol from a central mean oscillation space, considered as acting from a modified Herz space into another one, we find conditions of their boundedness. The sharpness of the result concerning commutators of the fractional Hardy-Littlewood operator is established.

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Acknowledgments

The authors express their gratitude to the anonymous referee for helpful remarks which allow to improve the text of the paper.

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Authors and Affiliations

  1. Saratov State University, 83 Astrahanskaya str., Saratov, 410012, Russia

    S. S. Volosivets

  2. Moscow Institute of Physics and Technology (State University), 9 Institutskii per., Moscow region, Dolgoprudny, 141700, Russia

    B. I. Golubov

Authors
  1. S. S. Volosivets
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  2. B. I. Golubov
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Corresponding authors

Correspondence to S. S. Volosivets or B. I. Golubov.

Additional information

Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 9, pp. 16–26.

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Volosivets, S.S., Golubov, B.I. Modified Fractional Hardy and Hardy-Littlewood Operators and Their Commutators. Russ Math. 63, 12–21 (2019). https://doi.org/10.3103/S1066369X19090020

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  • DOI: https://doi.org/10.3103/S1066369X19090020

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