数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (4): 1263-1274.doi: 10.1007/s10473-021-0414-8

• 论文 • 上一篇    下一篇

A GENERALIZATION OF BOYD'S INTERPOLATION THEOREM

Kwok-Pun HO   

  1. Department of Mathematics and Information Technology, the Education University of Hong Kong, Hong Kong, China
  • 收稿日期:2020-04-17 修回日期:2020-09-16 出版日期:2021-08-25 发布日期:2021-09-01
  • 作者简介:Kwok-Pun HO,E-mail:vkpho@eduhk.hk

A GENERALIZATION OF BOYD'S INTERPOLATION THEOREM

Kwok-Pun HO   

  1. Department of Mathematics and Information Technology, the Education University of Hong Kong, Hong Kong, China
  • Received:2020-04-17 Revised:2020-09-16 Online:2021-08-25 Published:2021-09-01

摘要: 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 rearrangementinvariant 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.

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 rearrangementinvariant 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.

中图分类号: 

  • 47B38