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On maximal functions for Mikhlin-Hoermander multipliers
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On maximal functions for Mikhlin-Hoermander multipliers
classification
math.CA
keywords
maximalfunctionsmultipliersboundboundsdilationsestimatesfunction
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Given Mikhlin-H\"ormander multipliers $m_i$, $i=1,..., N$, with uniform estimates we prove an optimal $\sqrt{\log(N+1)}$ bound in $L^p$ for the maximal function $\sup_i|\cF^{-1}[m_i\hat f]|$ and related bounds for maximal functions generated by dilations.
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