We show that if the Hardy–Littlewood maximal operator is bounded on a separable Banach function space \(X({\mathbb {R}})\) and on its associate space \(X'({\mathbb {R}})\), then the space \(X({\mathbb {R}})\) has an unconditional wavelet basis. This result extends previous results by Soardi (Proc Am Math Soc 125:3669–3673, 1997) for rearrangement-invariant Banach function spaces with nontrivial Boyd indices and by Fernandes et al. (Banach Center Publ 119:157–171, 2019) for reflexive Banach function spaces. We specify our result to the case of Lorentz spaces \(L^{p,q}({\mathbb {R}},w)\), \(1<p<\infty \), \(1\le q<\infty \) with Muckenhoupt weights \(w\in A_p({\mathbb {R}})\).

我们表明，如果Hardy–Littlewood极大算子在可分离的Banach函数空间\（X（{\ mathbb {R}}）\）及其关联空间\（X'（{\ mathbb {R}}）上有界\），则空间\（X（{\ mathbb {R}}）\）具有无条件小波基。该结果扩展了Soardi（Proc Am Math Soc 125：3669–3673，1997）先前关于具有非平凡Boyd指数的重排不变Banach函数空间以及Fernandes等人的先前结果。（Banach Center Publ 119：157–171，2019）用于自反Banach函数空间。我们以Lorentz空间\（L ^ {p，q}（{\ mathbb {R}}，w）\），\（1 <p <\ infty \），\（1 \ le q <\ infty \）带有Muckenhoupt权重\（w \ in A_p（{\ mathbb {R}}）\）。