A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents. (21st May 2015)

• Record Type: Journal Article
• Authors: Fiorenza, Alberto
• Other Names: Hudzik Henryk Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-05-21
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/581064
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : It is proven that if1 ≤ p ( · ) < ∞ in a bounded domainΩ ⊂ R n and ifp ( · ) ∈ EX P a ( Ω ) for somea > 0, then givenf ∈ L p ( · ) ( Ω ), the Hardy-Littlewood maximal function off, M f, is such thatp ( · ) log ( M f ) ∈ EX P a / ( a + 1 ) ( Ω ) . Becausea / ( a + 1 ) < 1, the thesis is slightly weaker than( M f ) λ p ( · ) ∈ L 1 ( Ω ) for someλ > 0 . The assumption thatp ( · ) ∈ EX P a ( Ω ) for somea > 0 is proven to be optimal in the framework of the Orlicz spaces to obtainp ( · ) log ( M f ) in the same class of spaces.