Talk:Bernstein's inequality (mathematical analysis)

Merger proposal

Re-suggesting that Bernstein's inequality (mathematical analysis) is merged into Bernstein's theorem (polynomials). The results of the articles are equivalent by a one-line application of the maximum modulus principle, and really should be viewed as the "same result". The example for derivatives would fit well into the framing of the latter article, so I can't see any obstacles in performing such a merge. — Preceding unsigned comment added by XRubbermaid (talk • contribs) 14:42, 17 March 2018 (UTC)

I agree. Also, the only "Bernstein inequality" I came across so far is

$\|P_{j}f\|_{L^{q}(\mathbb {R} ^{d})}\leq C2^{jd({\frac {1}{p}}-{\frac {1}{q}})}\|P_{j}f\|_{L^{p}(\mathbb {R} ^{d})}$

where $P_{j}$ is the Littlewood-Paley projector.

Similar inequalities (with this name) are mentioned in exercise 2.3.11 in Grafakos, Classical Fourier analysis, and at page 2, point LP 4, here:[1], and in the Lemma 5.4 here: [2].

Gim²y (talk) 14:13, 5 April 2018 (UTC)

  Y Merger complete. Klbrain (talk) 07:18, 13 July 2019 (UTC)