%A Kwok-Pun HO %T A GENERALIZATION OF BOYD'S INTERPOLATION THEOREM %0 Journal Article %D 2021 %J Acta mathematica scientia,Series B %R 10.1007/s10473-021-0414-8 %P 1263-1274 %V 41 %N 4 %U {http://121.43.60.238/sxwlxbB/CN/abstract/article_16477.shtml} %8 2021-08-25 %X 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.