6533b81ffe1ef96bd12785ca

RESEARCH PRODUCT

Smoothing properties of the discrete fractional maximal operator on Besov and Triebel-Lizorkin spaces

Heli TuominenToni Heikkinen

subject

Pure mathematicsGeneral MathematicsMetric measure spaceSpace (mathematics)Triebel–Lizorkin spaceMeasure (mathematics)Triebel-Lizorkin spaceFOS: Mathematics46E35Birnbaum–Orlicz spaceLp spaceBesov spacefractional Sobolev spaceMathematicsMathematics::Functional Analysista111Mathematical analysisFractional Sobolev spaceFunctional Analysis (math.FA)Fractional calculusMathematics - Functional Analysismetric measure space42B25 46E35fractional maximal functionBesov spaceInterpolation spaceFractional maximal function42B25

description

Motivated by the results of Korry, and Kinnunen and Saksman, we study the behaviour of the discrete fractional maximal operator on fractional Hajlasz spaces, Hajlasz-Besov, and Hajlasz-Triebel-Lizorkin spaces on metric measure spaces. We show that the discrete fractional maximal operator maps these spaces to the spaces of the same type with higher smoothness. Our results extend and unify aforementioned results. We present our results in a general setting, but they are new already in the Euclidean case.

yearjournalcountryeditionlanguage
2013-01-21
http://arxiv.org/abs/1301.4819