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A generalised integral is used to obtain a Fourier multiplier relation for Calderón-Zygmund operators on L1(Rn). In particular we conclude that an operator in our class is injective on L1(Rn) if it is injective on L2(Rn).

A multiplier relation for Calderón-Zygmund operators on 𝐿¹({ℝ}ⁿ)