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 language | English |
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Pages (from-to) | 1263-1274 |
Journal | Acta Mathematica Scientia |
Volume | 41 |
Issue number | 4 |
Early online date | 01 Jun 2021 |
DOIs | |
Publication status | Published - Jul 2021 |
Citation
Ho, K.-P. (2021). A generalization of boyd’s interpolation theorem. Acta Mathematica Scientia, 41(4), 1263-1274. doi: 10.1007/s10473-021-0414-8Keywords
- Interpolation of operator
- Quasilinear operator
- Rearrangement-invariant function space
- Spherical fractional maximal function
- Fractional maximal commutator
- Generalized Lorentz space