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Estimating integrals
Add and subtract something nearby that is simpler
Bound by a Riemann sum
Bound the integrand by something simpler
Bound your integral by its base times its height
Control level sets
Divide and conquer
Dyadic decomposition
General methods for estimating integrals
Geometric view of Hölder's inequality
How to use the Cauchy-Schwarz inequality
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Littlewood-Paley heuristic for derivative
Geometric view of Hölder's inequality
Diagonal arguments
Finding an interval for rational numbers with a high denominator
Try to prove a stronger result
Use self-similarity to get a limit from an inferior or superior limit.
Prove a consequence first
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