Let $f\in L^p(\mathbb R^2)$ for all $p\in[1,\bar p)$. Consider $$ g(y):=\int_{\mathbb R}f(x,y)\,dx \;.$$ Can I say that $g\in L^p(\mathbb R)$ for the same values of $p$ ?
2026-05-14 08:51:11.1778748671
Integral of an $L^p(\mathbb R^2)$ function is in $L^p(\mathbb R)$?
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