Wavelet Bases in Banach Function Spaces

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

Keywords:

• Mathematics
• Wavelet
• Function space
• Pure mathematics

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