Alignment like in align environment

Question

Does anyone know how to get the following alignment?

Answer 1

Here's a realization: I use split with an alignment point inside the first expression. For the second long line I use multlined with a width of 80% of the full display width.

\documentclass{article}
\usepackage{mathtools}

\begin{document}
\begin{equation*}
\begin{split}
\bigl\|(r_{\!B_i}^2L^k)&g^{}_{i,K_1,K_2,K_3}\bigr\|_{L^2(U_j(B_i))}
\\[2\jot]
  &\le
   \begin{multlined}[t][.8\displaywidth]
   \mu^{-1}\lvert\lambda_i\rvert r_{\!B_i}^{2M}
   \biggl\|\int_0^{K_1}\Bigl(\frac{t}{r^{}_{\!B_i}}\Bigr)^{\!2M-2k}
     (t^2L)^{k+1}e^{-(M+1)t^2L}\cdot{}
   \\
   \Bigl(\bigl[t^2Le^{-t^2L}a_i]\bigr]
   \chi^{}_{L^2(\Omega^{(1)}_{x_0,i,j,K_3})}\Bigr)
   \frac{dt}{t}\biggr\|_{L^2(U_j(B_i))}
   \end{multlined}
\\[2\jot]
  &\le
   C\mu^{-1}\lvert\lambda_i\rvert r_{\!B_i}^{2M}
   \int_0^{K_1}\Bigl(\frac{t}{r^{}_{\!B_i}}\Bigr)^{\!2M-2k}
   \bigl\|t^2Le^{-t^2L}a_i\bigr\|_{L^2(\Omega^{(1)}_{x_0,i,j,K_3})}
   \frac{dt}{t}
\end{split}
\end{equation*}
\end{document}

Note some of the fine points.

1. The B_i subscript to r is backed up slightly with \! in order to avoid a big gap

2. When a symbol has an uppercase subscript, a dummy superscript ^{} is added to move lower the subscript.

3. Smaller fences are used everywhere except around the integral.

4. The exponents to big ) are moved left with \!