
Let \(\omega\) (x) be a positive locally integrable weight on [0,1]. Discussed are conditions on \(\omega\) necessary and sufficient for the (dyadic) Hardy-Littlewood maximal function to map L log L(w dx) into \(L^ 1(\omega\) dx) or into weak \(L^ 1\).
Maximal functions, Littlewood-Paley theory, positive locally integrable weight, Hardy-Littlewood maximal function
Maximal functions, Littlewood-Paley theory, positive locally integrable weight, Hardy-Littlewood maximal function
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