Geodesic
On a converse inequality for maximal functions in Orlicz spaces
Studia Mathematica, Tome 118 (1996) no. 1, pp. 1-10
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Let $Φ(t) = ʃ_{0}^{t} a(s)ds$ and $Ψ(t) = ʃ_{0}^{t} b(s)ds$, where a(s) is a positive continuous function such that $ʃ_{1}^{∞} a(s)/s ds = ∞$ and b(s) is quasi-increasing and $lim_{s→∞}b(s) = ∞$. Then the following statements for the Hardy-Littlewood maximal function Mf(x) are equivalent: (j) there exist positive constants $c_1$ and $s_{0}$ such that $ʃ_{1}^{s} a(t)/t dt ≥ c_{1}b(c_{1}s)$ for all $s ≥ s_{0}$; (jj) there exist positive constants $c_2$ and $c_3$ such that $ʃ_{0}^{2π} Ψ((c_2)/(|⨍|_{
DOI : 10.4064/sm-118-1-1-10
Keywords: Hardy-Littlewood maximal function, Orlicz space 
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H. Kita. On a converse inequality for maximal functions in Orlicz spaces. Studia Mathematica, Tome 118 (1996) no. 1, pp. 1-10. doi: 10.4064/sm-118-1-1-10

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