Let's say the function f = X(-3,3] L (R) is given. Find real number x and...

 

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Let's say the function f = X(-3,3] L (R) is given. Find real number x and positive number r. Also find the Hardy-Littlewood maximum function and explain why. Also, check that the 3||f1 m({xER: (Hf)(x) > a}) a is established for any (Ar\f\)(x)=2(x-x+r) |f(t)\dt for any (Hf)(x) = sup(Ar|f(x) for any xR 1 018 Hardy Littlewood ine quality Let's say the function f = X(-3,3] L (R) is given. Find real number x and positive number r. Also find the Hardy-Littlewood maximum function and explain why. Also, check that the 3||f1 m({xER: (Hf)(x) > a}) a is established for any (Ar\f\)(x)=2(x-x+r) |f(t)\dt for any (Hf)(x) = sup(Ar|f(x) for any xR 1 018 Hardy Littlewood ine quality