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Maximal functions associated with families of homogeneous curves: L^p bounds for ple 2
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Maximal functions associated with families of homogeneous curves: L^p bounds for ple 2
classification
math.CA
keywords
maximalcurvesfunctionshomogeneousalongassociatedboundsconsider
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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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