We know that for a good summability kernel ${k_{n}}$: $k_{n}*f$ converges to f in $L^p$ norm for 1 <= p < $\infty$. But I have trouble finding a counter-example for the case p = $\infty$. Can someone please help me with this one ?
Best regards
2026-04-09 17:27:00.1775755620
An example of a function f whose Cesaro sum series doesn't converge to f in the $L^\infty$ norm
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The answer to my question was pretty simple (after giving it some thought): any bounded function on the circle with a set of discontinuities of measure non zero would do the trick !