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Boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents

Abstract

We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents \(\dot K_{p( \cdot ),q( \cdot )}^{\alpha ( \cdot )}\), such as some sublinear operators, the fractional integral and its commutator.

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Acknowledgements

The authors would like to express their deep gratitude to the anonymous referees for their careful reading of the manuscript and their comments and suggestions. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11671397, 12071473).

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Correspondence to Zongguang Liu.

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Yu, X., Liu, Z. Boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents. Front. Math. China 16, 211–237 (2021). https://doi.org/10.1007/s11464-021-0897-6

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Keywords

  • Sublinear operator
  • fractional integral
  • commutator
  • homogeneous Herz space
  • variable exponent

MSC2020

  • 42B20
  • 42B35