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Keywords:
weight; weak type inequality; Hardy-Littlewood maximal function; Orlicz class
weight; weak type inequality; Hardy-Littlewood maximal function; Orlicz class
Summary:
We collect known and prove new necessary and sufficient conditions for the weighted weak type maximal inequality of the form $$ \Phi _{1} (\lambda ) \varrho ( \{x\in X\colon M_\mu f (x) > \lambda \} ) \le c \int _X \Phi _{2} (c | {f(x)} | ) \sigma (x) {\rm d} \mu (x), $$ which extends some known results.
References:
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