If f: R R is periodic on R and integrable on [-Ï, Ï], prove that the Cesaro

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If f: R †’ R is periodic on R and integrable on [-Ï€, Ï€], prove that the Cesaro means of Sf are uniformly bounded; that is, there is an M > 0 such that
|(ON f)(x)| < M

for all x ˆˆ R and N ˆˆ N.

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