Szegő inequality

In functional analysis, a mathematical discipline, the Szegő inequality or Pólya–Szegő inequality, named after George Pólya and Gábor Szegő, states that if

1\leq p<+\infty

and

u:\mathbb {R} ^{n}\rightarrow \mathbb {R} ^{+}{\text{ in }}W^{1,p}(\mathbb {R} ^{n}),

then

\int _{\mathbb {R} ^{n}}|\nabla u^{*}|^{p}\,d{\mathcal {H}}^{n}\leq \int _{\mathbb {R} ^{n}}|\nabla u|^{p}\,d{\mathcal {H}}^{n},

See also