WordPress is notorious for not accepting **\begin{align} … \end{align}** as it is not in math mode.

I have updated the LaTeX to WordPress Converter to change **\begin{align} … \end{align} **to **$l atex\begin{aligned} … \end{aligned}$** which works in WordPress.

## Test Input:

Let $h=\chi_{[0,1]}$, the characteristic function of $[0,1]$. We have $\|\chi_{[0,1]}\|_\infty=1$, so $\chi_{[0,1]}\in L^\infty$. Then,

\begin{align*}

(Hh)(x)&=\frac{1}{\pi}\int_0^1\frac{1}{x-t}\ dt\\

&=\frac{1}{\pi}[-\ln|x-t|]_0^1\\

&=\frac{1}{\pi}\ln\frac{|x|}{|x-1|}.

\end{align*}

As $x\to 1$, $(Hh)(x)\to\infty$. Thus, $Hh$ is an unbounded function, so $H$ is not bounded as a map: $L^\infty\to L^\infty$.

\[\frac{a}{b}=c\]

## Test Output:

Let , the characteristic function of . We have , so . Then,

As , . Thus, is an unbounded function, so is not bounded as a map: .

Thanks for this service !

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You are welcome! I use it personally to blog, it saves a lot of time.

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