I cannot write less and greater symbol. How can ı write?

Question

how can ı write this symbol. If you help me this problem thank you very much.

Answer 1

Here there is the example of your image using a macro named \hupdown: the symbol is \gtrless.

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\newcommand\hupdown[1]{\mathop{\operatorname{#1}}}
\begin{document}
[\hupdown{\scriptstyle \gtrless}_{\mathcal{H}_0}^{\mathcal{H}_1}]
\end{document}

Or if you prefer you can choose this MWE reducing the size of the symbol with \scriptscriptstyle:

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\newcommand\hupdown[1]{\mathop{\operatorname{#1}}}
\begin{document}
[\hupdown{ \gtrless}_{\scriptscriptstyle\mathcal{H}_0}^{\scriptscriptstyle\mathcal{H}_1}]
\end{document} 

Addendum after a deleted answer that it is an edit on the question of the user.

\documentclass[a4paper,12pt]{article}
\usepackage{newtxtext,newtxmath}
\usepackage[bb = boondox]{mathalfa}
\newcommand\hupdown[1]{\mathop{\operatorname{#1}}} 
\DeclareSymbolFont{largesymbolsCM}{OMX}{cmex}{m}{n}
\let\txsum\sum
\let\sum\relax
\DeclareMathSymbol{\sum}{\mathop}{largesymbolsCM}{"50}
\DeclareMathAlphabet{\pazocal}{OMS}{zplm}{m}{n}
\begin{document}
[\mathbb{T}{i}(\boldsymbol{y}{i})=\sum_{n=1}^{N}{|\boldsymbol{y}{i}}[n]{{|}^{2}}\hupdown{ \gtrless}{\scriptscriptstyle\pazocal{H}_0}^{\scriptscriptstyle\pazocal{H}_1}\lambda]
\end{document}

Addendum of the 2021/09/08. Another alternative given from @egreg in this question here Underset and Overset Together is to use the command \overunderset{....}{....}{....} without a macro:

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath} % for \overunderset command
\usepackage{newtxtext,newtxmath}
\usepackage[bb = boondox]{mathalfa}
\DeclareSymbolFont{largesymbolsCM}{OMX}{cmex}{m}{n}
\let\txsum\sum
\let\sum\relax
\DeclareMathSymbol{\sum}{\mathop}{largesymbolsCM}{"50}
\DeclareMathAlphabet{\pazocal}{OMS}{zplm}{m}{n}
\begin{document}
[\mathbb{T}{i}(\boldsymbol{y}{i})=\sum_{n=1}^{N}{|\boldsymbol{y}_{i}}[n]{{|}^{2}}\overunderset{\pazocal{H}_0}{\pazocal{H}_1}{\gtrless}\lambda]
\end{document}