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I see this proof on http://www.math.uiowa.edu/~lwang/cccalderon.pdf and I couldn't understand what he did. If $||f||_{L^p(B_{4})} = \delta$ is small and the measure $|\{ x \in B_1; M(|D^2u|^2)>N_1^2 \}| \leq \epsilon|B_1| $. Then, we have:

$$\sum_{i=1}^{+ \infty} (N_{1})^{ip}|\{M(|f|^2) > \delta^2 (N_{1})^{2i}\}| \leq \frac{pN^{p}}{\delta^{p}(N-1)}||f||_{{L^p}(B_{1})}^{p}$$

Someone could help me? Here M denotes the maximal function of Hardy Littlewood.

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    $\begingroup$ What is $u$? It does not appear in the inequality. $\endgroup$
    – username
    Commented May 22, 2014 at 11:04

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