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hilbert transforms along curves

Proceedings of the Edinburgh Mathematical Society (1)

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1 results

Maximal functions associated with families of homogeneous curves: Lp bounds for P ≤ 2
Part of
- Harmonic analysis in several variables
- Integral transforms, operational calculus
Shaoming Guo, Joris Roos, Andreas Seeger, Po-Lam Yung
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 63 / Issue 2 / May 2020

Published online by Cambridge University Press:

03 February 2020, pp. 398-412
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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.