A generalization of boyd’s interpolation theorem

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Abstract

Boyd’s interpolation theorem for quasilinear operators is generalized in this paper, which gives a generalization for both the Marcinkiewicz interpolation theorem and Boyd’s interpolation theorem. By using this new interpolation theorem, we study the spherical fractional maximal functions and the fractional maximal commutators on rearrangement-invariant quasi-Banach function spaces. In particular, we obtain the mapping properties of the spherical fractional maximal functions and the fractional maximal commutators on generalized Lorentz spaces. Copyright © 2021 Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences.
Original languageEnglish
Pages (from-to)1263-1274
JournalActa Mathematica Scientia
Volume41
Issue number4
Early online date01 Jun 2021
DOIs
Publication statusPublished - Jul 2021

Citation

Ho, K.-P. (2021). A generalization of boyd’s interpolation theorem. Acta Mathematica Scientia, 41(4), 1263-1274. doi: 10.1007/s10473-021-0414-8

Keywords

  • Interpolation of operator
  • Quasilinear operator
  • Rearrangement-invariant function space
  • Spherical fractional maximal function
  • Fractional maximal commutator
  • Generalized Lorentz space

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