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. - In: JOURNAL OF FUNCTION SPACES. - ISSN 2314-8896. - 2015:Article ID 581064(2015), pp. 1-5. [10.1155/2015/581064]
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
