Article contents
On weighted estimates for Stein's maximal function
Published online by Cambridge University Press: 17 April 2009
Abstract
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
- Copyright
- Copyright © Australian Mathematical Society 1996
References
REFERENCES
- 5
- Cited by