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arXiv · 1906.05997

Maximal functions associated with families of homogeneous curves: $L^p$ bounds for $p\le 2$

Shaoming Guo·Joris Roos·Andreas Seeger·Po-Lam Yung
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Abstract

Let $M^{(u)}$, $H^{(u)}$ be the maximal operator and Hilbert transform along the parabola $(t, ut^2) $. For $U\subset(0,\infty)$ we consider $L^p$ estimates for the maximal functions $\sup_{u\in U}|M^{(u)} f|$ and $\sup_{u\in U}|H^{(u)} f|$, when $1<p\le 2$. The parabolae can be replaced by more general non-flat homogeneous curves.

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Shaoming Guo, Joris Roos, Andreas Seeger, Po-Lam Yung. 2019-12-03. Maximal functions associated with families of homogeneous curves: $L^p$ bounds for $p\le 2$. https://doi.org/10.1017/s0013091519000439

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