Limits under multiple \sum

Something like:

\mathop{\sum_{j=1}^{\infty}\sum_{k=1}^{\infty}}_{j>k}

maybe?

Looks like this:

Or if you want it on the same line as j=1 and k=1, then maybe:

\mathop{\sum^{\infty}\sum^{\infty}}_{j=1\ j>k\ k=1}

There is an equivalent alternative.

\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
\usepackage{mathtools}

\begin{document}
  \[
    \underset{j>k}{\sum_{j=1}^{\infty}\sum_{k=1}^{\infty}}
  \]
\end{document}