Abstract
We prove that limK α*f(x)=f(x) at all he Lebesque points offεL p for some approximate identities {K α}, and that for every approximate identity {ϕλ} of dilation type defined by a nonnegative kernel φεL 1, the corresponding convergence at Lebesgue points implies that the kernel has an integrable radial majorant.
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Cerdà, J.L., Sueiro, J.M. Approximate identities and convergence at Lebesgue points. Rend. Circ. Mat. Palermo 32, 5–12 (1983). https://doi.org/10.1007/BF02851097
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DOI: https://doi.org/10.1007/BF02851097