Sum of Lp spaces
= Sum of Lp spaces
{title2=$L^{p_0}+L^{p_1}$}
The sum consists of <measurable functions> $f=g+h$ with $g\in L^{p_0}$ and $h\in L^{p_1}$, with <norm> $\inf_{f=g+h}(\|g\|_{p_0}+\|h\|_{p_1})$. It is a <Banach space>. One construction identifies it with the quotient of $L^{p_0}\oplus_1L^{p_1}$ by the closed kernel of the addition map. Bounded endpoint operators are therefore bounded on the corresponding sum spaces.