# Tag Info

Accepted

### Inequality with decreasing rearrangement and non-decreasing function

• 85.1k
Accepted

No (if $c$ cannot depend on $f^*$ or $g$). Indeed, let $h:=f^*/g$. Then $h$ can be any positive function and the inequality in question can be rewritten as $$lhs:=\Big(\int_0^\infty h(s)^{p'}ds\Big)^{... • 85.1k 6 votes ### How was Claim 5 in "A non-linear generalisation of the Loomis–Whitney inequality and applications" thought up? As Dan Romik points out, this technique is relatively old folklore by now. Terry Tao calls this the "tensor power trick" in a blog post dedicated to the subject; the two elementary ... 6 votes ### How was Claim 5 in "A non-linear generalisation of the Loomis–Whitney inequality and applications" thought up? An instance of this idea of killing an unwanted factor in an inequality by considering an inequality for k-th powers and then taking the limit as k\to\infty appears in the proof of the Kraft-... • 2,226 6 votes Accepted ### Is the extension (dual restriction) operator on any smooth hypersurface a solution to some PDE? Your question was basically answered by David Roberts in the comments, but let me write a few more words. Given a constant coefficient linear differential operator of degree N$$ L = \sum_{|\alpha| \...
• 32.5k
Stupid me! I posted my own answer anyway for other fledglings like me or for anyone to double check my proof! ($f_{1,i}$ is $f_1$ restricted to a small compact subset indexed as $i$. Similarly to \$f_{...