\documentclass{article}
\usepackage{latexml}
\lxDeclare[role=OPERATOR]{$D$}

\begin{document}
% Test a nested application of an operator over a trigfunction
$ D D \sin x $
%
% Test explicitly applying an operator over
%   an argument composed of multiple "bare" pieces
\iflatexml\makeatletter
$ D \lx@ApplyFunction x \times y \times z $
\makeatother\fi
%
\end{document}