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Best monotone approximation and the Hardy-Littlewood maximal function |
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| Authors: | J J Swetits S E Weinstein |
| Institution: | (1) Old Dominion University, U. S. A. |
| Abstract: | If f∈L20, 1] and g*∈L20, 1] is the best non-decreasing approximation to f, then it's shown that ‖f−g*‖2=‖f−θ(f)‖2, where θ(f) denotes the Hardy-Littlewood maximal function of f. |
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