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

Author:

17 April 2002

journal article
research article
Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society

Vol. 65 (2) , 253-258
DOI:10.1017/s0004972700020293

Abstract

Dedicated to Professor Kôzô Yabuta on the occasion of his 60th birthdayJ. Kinnunen proved that of P > 1, d ≤ 1 and f is a function in the Sobolev space W^1,P(R^d), then the first order weak partial derivatives of the Hardy-Littlewood maximal function ℳf belong to L^P(R^d). We shall show that, when d = 1, Kinnunen's result can be extended to the case where P = 1.

Keywords

MAXIMAL
HARDY
LITTLEWOOD
SOBOLEV SPACE
ORDER WEAK
KINNUNEN'S RESULT
FUNCTION ℳF
60TH BIRTHDAY
PROFESSOR KÔZÔ

This publication has 2 references indexed in Scilit:

Elliptic Partial Differential Equations of Second Order
2001
The hardy-littlewood maximal function of a sobolev function
Israel Journal of Mathematics, 1997