Article
Keywords:
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:
[4] Gogatishvili, A., Kokilashvili, V.:
Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. I. Georgian Math. J. 2 (1995), 361-384.
DOI 10.1515/GMJ.1995.361 |
MR 1344301 |
Zbl 0836.42012