Singular and fractional integral operators on preduals of Campanato spaces with variable growth condition

Abstract

We investigate the boundedness of singular and fractional integral operators on generalized Hardy spaces defined on spaces of homogeneous type, which are preduals of Campanato spaces with variable growth condition. To do this we introduce molecules with variable growth condition. Our results are new even for ℝn case.

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Acknowledgements

This work was supported by Grant-in-Aid for Scientific Research (B) (Grant No. 15H03621), Japan Society for the Promotion of Science. The author thanks the referees for their careful reading and useful comments.

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Correspondence to Eiichi Nakai.

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Dedicated to the memory of Professor CHENG MinDe on the occasion of the centenary of his birth

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Nakai, E. Singular and fractional integral operators on preduals of Campanato spaces with variable growth condition. Sci. China Math. 60, 2219–2240 (2017). https://doi.org/10.1007/s11425-017-9154-y

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Keywords

  • singular integral
  • fractional integral
  • Hardy space
  • Campanato space
  • variable exponent
  • space of homogeneous type

MSC(2010)

  • 42B30
  • 46E30
  • 42B20
  • 43A17