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On an integral of Marcinkiewicz

On an integral of Marcinkiewicz

Let/(0) be a function of period 2w and class LT, p>l.By F( 6) is meant a primitive of/(f), i.e., F(6) = f f(x)dx + C. J o Marcinkiewicz [3] defined the function Pr(6) = j J \[F(B + t) + F(0 -0 -2F(d)Y/r+l)dtl ( r * rF(d + t) + …