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a few missing braces
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fpvandoorn committed Apr 3, 2024
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6 changes: 3 additions & 3 deletions blueprint/src/chapter/main.tex
Original file line number Diff line number Diff line change
Expand Up @@ -4948,11 +4948,11 @@ \section{Separated Trees}
\eqref{T*Hölder1} \le \frac{2^{151a^3}}{\mu(B(c(\fp), 4D^{s(\fp)}))} \left(\frac{\rho(y,y')}{D^{s(\fp)}}\right)^{\tau'} \int_{E(\fp)}|g(x)| \, \mathrm{d}\mu(x)\,.
$$

If $y,y' \notin B(c(\fp), 5D^{s(\fp)})$, then $T_\fp^*g(y) = T_\fp^*g(y') = 0$, by \eqref{eq Ks supp t} and the triangle inequality. Then \eqref{T*Hölder2} holds.
If $y,y' \notin B(c(\fp), 5D^{s(\fp)})$, then $T_{\fp}^*g(y) = T_{\fp}^*g(y') = 0$, by \eqref{eq Ks supp t} and the triangle inequality. Then \eqref{T*Hölder2} holds.

Finally, if $y \in B(c(\fp), 5D^{s(\fp)})$ and $y' \notin B(c(\fp), 5D^{s(\fp)})$, then
$$
|e(Q(\fu)(y)) T_{\fp}^* g(y) - e(Q(\fu)(y')) T_{\fp}^* g(y')| = |T_\fp^* g(y)|
|e(Q(\fu)(y)) T_{\fp}^* g(y) - e(Q(\fu)(y')) T_{\fp}^* g(y')| = |T_{\fp}^* g(y)|
$$
$$
\le \int_{E(\fp)} |K_{s(\fp)}(x,y)| |g(x)| \, \mathrm{d}\mu(x)\,.
Expand Down Expand Up @@ -4981,7 +4981,7 @@ \section{Separated Trees}
$$
Plugging this in and using $a \ge 4$, we get
$$
|T_\fp^* g(y)| \le \frac{2^{103a^3}}{\mu(B(c(\fp), 4D^{s(\fp)}))} \left(\frac{\rho(y,y')}{D^{s(\fp)}}\right)^{\tau'} \int_{E(\fp)} |g(x)| \, \mathrm{d}\mu(y)\,,
|T_{\fp}^* g(y)| \le \frac{2^{103a^3}}{\mu(B(c(\fp), 4D^{s(\fp)}))} \left(\frac{\rho(y,y')}{D^{s(\fp)}}\right)^{\tau'} \int_{E(\fp)} |g(x)| \, \mathrm{d}\mu(y)\,,
$$
which completes the proof of the lemma.
\end{proof}
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2 changes: 1 addition & 1 deletion docs/_layouts/default.html
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Expand Up @@ -45,7 +45,7 @@ <h2 class="project-tagline">{{ page.description | default: site.description | de
<footer class="site-footer">
{% if site.github.is_project_page %}
<span class="site-footer-owner"><a href="{{ site.github.repository_url }}">{{ site.github.repository_name }}</a>
is maintained by Terence Tao from UCLA and Yaël Dillies from the University of Cambridge. Visit the repository on GitHub for the list of contributors.</span>
is maintained by Floris van Doorn. Visit the repository on GitHub for the list of contributors.</span>
{% endif %}
</footer>
</main>
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