Article contents
Maximal functions associated with families of homogeneous curves: Lp bounds for P ≤ 2
Published online by Cambridge University Press: 03 February 2020
Abstract
Let M(u), H(u) be the maximal operator and Hilbert transform along the parabola (t, ut2). For U ⊂ (0, ∞) we consider Lp estimates for the maximal functions sup u∈U|M(u)f| and sup u∈U|H(u)f|, when 1 < p ≤ 2. The parabolas can be replaced by more general non-flat homogeneous curves.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © Edinburgh Mathematical Society 2020
Footnotes
Current address: Mathematical Sciences Institute, Australian National University, Canberra, ACT 2600, Australia; polam.yung@anu.edu.au.
References
- 5
- Cited by