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.

中文翻译：

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博伊德插值定理的推广

本文对拟线性算子的 Boyd 插值定理进行了推广，给出了 Marcinkiewicz 插值定理和 Boyd 插值定理的推广。通过使用这个新的插值定理，我们研究了重排不变拟巴拿赫函数空间上的球面分数极大函数和分数极大交换子。特别地，我们获得了球面分数极大函数和分数极大交换子在广义洛伦兹空间上的映射性质。