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A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function

Published online by Cambridge University Press:  17 April 2009

Hitoshi Tanaka
Hitoshi Tanaka
Affiliation:
Department of Mathematics, Gakushuin University, 1–5–1 Mejiro, Toshima-Ku, Tokyo 171–8588, Japan, e-mail: [email protected]
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Abstract

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Dedicated to Professor Kôzô Yabuta on the occasion of his 60th birthday

J. Kinnunen proved that of P > 1, d ≤ 1 and f is a function in the Sobolev space W1,P(Rd), then the first order weak partial derivatives of the Hardy-Littlewood maximal function ℳf belong to LP(Rd). We shall show that, when d = 1, Kinnunen's result can be extended to the case where P = 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 2 , April 2002 , pp. 253 - 258
Copyright
Copyright © Australian Mathematical Society 2002

References

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