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On weighted estimates for Stein's maximal function

Published online by Cambridge University Press:  17 April 2009

Hendra Gunawan
Hendra Gunawan
Affiliation:
Department of Mathematics, Institut Teknologi Bandung, Ganesha 10, Bandung 40132, Indonesia
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Abstract

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Let φ denote the normalised surface measure on the unit sphere Sn−1. We shall be interested in the weighted Lp estimate for Stein's maximal function Mφf, namely

where w is an Ap weight, especially for 1 < p ≤ 2. Using the Mellin transformation approach, we prove that the estimate holds for every weight wδ where w ∈ Ap and 0 ≤ δ < (p(n − 1) − n)/(n(p − 1)), for n ≥ 3 and n/(n − 1) < p ≤ 2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 1 , August 1996 , pp. 35 - 39
Copyright
Copyright © Australian Mathematical Society 1996

References

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