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On $L^p$ norms of maximal operators
We study the exact $L^p$ norms for a number of maximal operators, which are prominent in harmonic analysis, semigroup theory, and probability. We prove that a strongly continuous positive symmetric sub-Markovian semigroup $(T_t)_{t\ge0}$ on a nonatomic $σ$-finite measure space $(X,\mathcal F,μ)$ has
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