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Fix typos in main.tex (#11)
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pitmonticone authored May 8, 2024
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4 changes: 2 additions & 2 deletions blueprint/src/chapter/main.tex
Original file line number Diff line number Diff line change
Expand Up @@ -7455,7 +7455,7 @@ \section{Proof of Cotlar's Inequality}
T_{0} g(x):=\sup_{0<r_1<1}\sup_{|x-x'|<r_1}\frac 1{2\pi} \left|\int_{r_1<|x'-y|<1}
g(y) \kappa(x'-y)\, dy\right|\, .
\end{equation}
We now write by the triangle inequaqlity
We now write by the triangle inequality
\begin{equation}\label{concretetstartriangle}
T_* g(x)\le \sup_{0<r_1<r_2<1}\sup_{|x-x'|<r_1}\frac 1{2\pi} \left|\int_{r_1<|x'-y|<1}g(y) \kappa(x'-y)\, dy\right|
\end{equation}
Expand Down Expand Up @@ -8293,7 +8293,7 @@ \section{Calder\'on-Zygmund Decomposition}
\end{proof}

\begin{proof}[Proof of Lemma \ref{lem-weak-1-1}]
Using Lemma \ref{lem-czd-func} for $f$ and $2^{-10}\alpha$, we obtain the deomposition
Using Lemma \ref{lem-czd-func} for $f$ and $2^{-10}\alpha$, we obtain the decomposition
$$f=g+\sum_j b_j$$
such that the properties \eqref{eq-gb-dec}-\eqref{eq-b-L1} are satisfied with $\gamma=2^{-10}$. For each $j$, let
\begin{equation}
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