Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces

By Jean Bourgain. 2011

139 citations recorded by the source corpus.

AbstractA new moment inequality is obtained for the eigenfunctions ϕ of the flat tours Πn. More specifically, it is known that the $p = \frac{{2n}} {{n - 1}} $ is almost uniformaly bounded. Simillar results are established for the periodiec Schrödinger group.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/32dbe8e2b53396ecfd7bc5287515301b1453abfa

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Restriction estimates using polynomial partitioning II (2016, methodology): “rol the contribution from the k-non-transverse balls. This inductive argument can be described most cleanly using the language of decoupling. Building on [BG], Bourgain proved a decoupling theorem in [B4] which implies that for each k-nontransverse ball BK2, kEfk2 Lp(B K2) . X τ∈S(BK2) kEfτk2 Lp(B K”
Strichartz estimates for Schrödinger equations on irrational tori (2013, methodology): “In the following, we establish another estimate on ‖f ∗ ΛM,s‖L2(I×Td), using the following lemma from Bourgain [3].”
The proof of the l 2 Decoupling Conjecture (2015, methodology): “It has been observed in [11] that Theorem 1.1 for a given p implies (6) for the same p .”
MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS (2013, background): “This causes a significant difficulty which may be resolved by using the more recent works [19] and [59] as we now explain.”
Aspects of Multilinear Harmonic Analysis Related to Transversality (2014, methodology): “ut the ﬁrst term. Unfortunately there is some loss in doing this which places some limit on the resulting progress; see [22]. For further applications of Theorem 4.1 and the Bourgain–Guth method, see [20], [21], [23], [52] and [36]. 5. Transversal multilinearharmonicanalysis: a bigger picture The ai”
Injections de Sobolev probabilistes et applications (2011, background): “On renvoie à [8, 9, 10] pour de nombreux autres résultats sur les fonctions propres du laplacien sur les tores.”
Strichartz estimates for the Schrödinger equation on irrational tori (2017, background): “if d = 2, θ(p) =    0, p ∈ [1, 4) , 2(p − 4) p+ 4 , p ∈ [4, 6) ,”
Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three (2015, background): “The relevant machinery that we now call decouplings showed its initial potential for applications in papers such as [17], [14], [16] and [4].”