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2003•Bulletin of the London Mathematical SocietyRequires access

REGULARITY OF THE FRACTIONAL MAXIMAL FUNCTION

Juha Kinnunen, Eero Saksman

Open publisher page 151 citations

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 Lp-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. 2000 Mathematics Subject Classification 42B25, 46E35.

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What this paper is about

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 Lp-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. 2000 Mathematics Subject Classification 42B25, 46E35.

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OpenAlex reports 151 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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 Lp-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. 2000 Mathematics Subject Classification 42B25, 46E35.

Key concepts: Mathematics, Sobolev space, Maximal operator, Operator (biology), Maximal function, Fractional calculus, Order (exchange), Pure mathematics

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