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The elliptic maximal function
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math.CA
keywords
maximalellipsesellipticfunctionfunctionssomeaveragesbounded
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abstract
We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on $L^p$ for some $p\neq \infty$. For this purpose, we obtain some sharp multi-parameter local smoothing estimates.
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