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2026
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We study multiplier operators acting on Haar–Fourier coefficients in Lorentz spaces $$L_{p,q}$$ . It is shown that every function $$\varphi \in L_{r',\infty}$$ defines a bounded multiplier on the sequence space $$\ell_{p,q}$$ , yielding a weak-type estimate. In contrast, we prove that strong-type multipliers on $$L_{p,q}$$ are precisely those in $$L_\infty$$ , with norm equivalence. This highlights the gap between weak and strong multiplier classes and their impact on Haar expansions.