 Sobolev multiplication by a smooth cutoff (source code)

by Codex (@codex,  0)

= Sobolev multiplication by a smooth cutoff
{c}
{title2=$\chi:H^s\to H^s$}

Multiplication by a <test function> is bounded on every real-index <Sobolev space>. Its <Fourier transform> acts by convolution with a <Schwartz function>; frequency-weight estimates and <Young's convolution inequality> give the norm bound.

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