Updated LaTeX to WordPress Converter

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 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{aligned}  (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{aligned}
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.
\displaystyle \frac{a}{b}=c

 

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About mathtuition88

http://mathtuition88.com
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2 Responses to Updated LaTeX to WordPress Converter

  1. nkpithwa says:

    Thanks for this service !

    Liked by 1 person

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