247A Lecture Notes 3: The Hardy-Littlewood Maximal Inequality
by Terence Tao · UCLA Department of Mathematics
Fifteen pages of Terence Tao's UCLA graduate harmonic analysis notes covering the Hardy-Littlewood maximal inequality: Vitali-type covering arguments, the weak-(1,1) bound, Marcinkiewicz interpolation to Lp, dyadic maximal functions, and the Lebesgue differentiation theorem.
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Graduate real-analysis lecture notes published as a blog post, proving the Hardy-Littlewood maximal inequality with covering and rising-sun arguments, then deducing the Lebesgue differentiation theorem, absolute continuity and bounded variation results, with many embedded exercises.
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