Geodesic
Necessary and sufficient conditions for the two-weight weak type maximal inequality in Orlicz class
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 79-85
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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.
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.
DOI : 10.21136/CMJ.2021.0320-20
Classification : 42B25, 46E30
Keywords: weight; weak type inequality; Hardy-Littlewood maximal function; Orlicz class 
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Ren, Yanbo; Ding, Shuang. Necessary and sufficient conditions for the two-weight weak type maximal inequality in Orlicz class. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 79-85. doi: 10.21136/CMJ.2021.0320-20

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