It is proven that if 1≤(⋅)<∞ in a bounded domain Ω⊂R and if (⋅)∈EXP(Ω) for some >0, then given ∈(⋅)(Ω), the Hardy-Littlewood maximal function of , , is such that (⋅)log() ∈ EXP/(+1)(Ω). Because /( + 1) < 1, the thesis is slightly weaker than ()(⋅) ∈ 1(Ω) for some > 0. The assumption that (⋅) ∈ EXP(Ω) for some > 0 is proven to be optimal in the framework of the Orlicz spaces to obtain (⋅)log() in the same class of spaces.

A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents

FIORENZA, ALBERTO
2015

Abstract

It is proven that if 1≤(⋅)<∞ in a bounded domain Ω⊂R and if (⋅)∈EXP(Ω) for some >0, then given ∈(⋅)(Ω), the Hardy-Littlewood maximal function of , , is such that (⋅)log() ∈ EXP/(+1)(Ω). Because /( + 1) < 1, the thesis is slightly weaker than ()(⋅) ∈ 1(Ω) for some > 0. The assumption that (⋅) ∈ EXP(Ω) for some > 0 is proven to be optimal in the framework of the Orlicz spaces to obtain (⋅)log() in the same class of spaces.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/609650
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