Abstract
We obtain sharp estimates for the localized distribution function of the dyadic maximal function M ϕ d , given the local L 1 norms of ϕ and of G ○ ϕ where G is a convex increasing function such that G ( x ) / x → + ∞ as x → + ∞ . Using this we obtain sharp refined weak type estimates for the dyadic maximal operator.
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