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BMO and variationsAs an extension of our class notes, we were asked to show that the function w=log(x) is a Bounded Mean Oscillation (BMO). First off, I believe. Typical examples of BMO-functions are of the form log|P| with P a polynomial on Rn. The space BMO is very important in modern harmonic analysis. Definition of VMO functions and maps. VMO is the completion of smooth functions in the BMO norm, namely, a real function f on X belongs to VMO(X.
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