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Czechoslovak Mathematical Journal, Vol. 72, No. 1, pp. 79-85, 2022

Necessary and sufficient conditions for the two-weight weak type maximal inequality in Orlicz class

Yanbo Ren, Shuang Ding

Received July 27, 2020.   Published online October 20, 2021.
Abstract:  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.
Keywords:  weight; weak type inequality; Hardy-Littlewood maximal function; Orlicz class
Classification MSC:  42B25, 46E30
DOI:  10.21136/CMJ.2021.0320-20
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Affiliations:   Yanbo Ren (corresponding author), School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, P. R. China, e-mail: ryb7945@sina.com; Shuang Ding, School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471000, P. R. China, e-mail: dingyouyou456@163.com
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