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A reverse weighted inequality for the Hardy-Littlewood maximal function in Orlicz spaces

Author： Kita H.

Publisher： Springer Publishing Company

ISSN： 0236-5294

Source： Acta Mathematica Hungarica, Vol.98, Iss.1-2, 2003-01, pp. : 85-101

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

Let Φ(t)= ∫_0^t a(s) ds and Ψ(t)= ∫_0^t b(s) ds, where a(s) is a positive continuous function such that ∫_0^1 frac{a(s)}{s} ds < ∞and ∫_1^{∞}frac{a(s)}{s} ds= +∞, and b(s) is an increasing function such that lim_{sto∞}b(s)= +∞. Letw be a weight function and suppose that w∈A₁∩ A_∞'. Then the following statements for the Hardy-Littlewood maximal function Mf(x) are equivalent:(I) there exist positive constants C ₁ and C ₂ such that 0;$$ ]]> (II) there exist positive constants C ₃ and C ₄ such that

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