Abstract
Let I be a fixed subinterval of R and let 1≤p<∞ be a fixed exponent. Suppose that f∈Lp(I) is an arbitrary function of integral zero and let f# be the BLO-based sharp maximal function of f. The paper contains the identification of the best constant Cp in the estimate‖f‖Lp≤Cp‖f#‖Lp. The proof rests on the explicit evaluation of the Bellman function associated with the above estimate.
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