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22 (a) Assume that both f and its maximal function Mf are in L'(RK). Prove that then f(x) = 0 a.e. . [m]. Hint: To

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22 (a) Assume that both f and its maximal function Mf are in L'(RK). Prove that then f(x) = 0 a.e. . [m]. Hint: To every other f e l'(R*) corresponds a constant c = df) >0 such that (Mf(x) > c|x|-* whenever | x | is sufficiently large. (b) Define f(x) = x-'(log x)-2 if 0 0 such that (Mf(x) > c|x|-* whenever | x | is sufficiently large. (b) Define f(x) = x-'(log x)-2 if 0

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