How to print the “essential supremum” operator

You probably want to declare a new math operator:

\documentclass{article}
\usepackage{amsmath}

\DeclareMathOperator*{\supess}{sup\,ess}

\begin{document}

\[
\supess_{0\leq x\leq 2\pi}
\]

\end{document}

This is more convenient than using \operatorname*{sup\,ess} (note that ~ is not the best here), because you may be requested to change the rendering into

(a notation more commonly used in document written in English), which can be accomplished by just changing one line

\DeclareMathOperator*{\supess}{ess\,sup}

without chasing for all appearances in the document.

I would use amsmath and \operatorname. While \mathrm uses normally the same font as the operators, one can be sure that this is true in all math setups. (The star leads to \limits):

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\[\operatorname*{sup~ess}_{0\leq x\leq 2\pi}\]

\end{document}

Variants are to use sup\,ess, and the \leq can be changed too. If needed a command like \supess can be defined with \DeclareMathOperator.

You can use the following:

\documentclass{article}

\begin{document}
\[\mathop{\mathrm{sup~ess}}\limits_{0\leq x\leq 2\pi}\]
\end{document}

with the result: