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REGULARITY OF THE FRACTIONAL MAXIMAL FUNCTION

  • JUHA KINNUNEN (a1) and EERO SAKSMAN (a2)

Abstract

The purpose of this work is to show that the fractional maximal operator has somewhat unexpected regularity properties. The main result shows that the fractional maximal operator maps $L^p$-spaces boundedly into certain first-order Sobolev spaces. It is also proved that the fractional maximal operator preserves first-order Sobolev spaces. This extends known results for the Hardy–Littlewood maximal operator.

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REGULARITY OF THE FRACTIONAL MAXIMAL FUNCTION

  • JUHA KINNUNEN (a1) and EERO SAKSMAN (a2)

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