Local Bounds for Singular Brascamp–Lieb Forms with Cubical Structure

Authors

Polona Durcik, Chapman UniversityFollow
Lenka Slavíková, Charles UniversityFollow
Chrisoph Thiele, Universität BonnFollow

Document Type

Article

Publication Date

9-27-2022

Abstract

We prove a range of L^p bounds for singular Brascamp-Lieb forms with cubical structure. We pass through sparse and local bounds, the latter proved by an iteration of Fourier expansion, telescoping, and the Cauchy-Schwarz inequality. We allow 2^m−1 < p ≤ ∞ with m the dimension of the cube, extending an earlier result that required p = 2^m. The threshold 2^m−1 is sharp in our theorems.

Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Mathematische Zeitschrift in 2022 following peer review. The final publication may differ and is available at Springer via https://doi.org/10.1007/s00209-022-03148-8.

A free-to-read copy of the final published article is available here.

Recommended Citation

Durcik, P., Slavíková, L. & Thiele, C. Local bounds for singular Brascamp–Lieb forms with cubical structure. Math. Z. (2022). https://doi.org/10.1007/s00209-022-03148-8

Peer Reviewed

1

Copyright

Springer