Chapman University Digital Commons

Title

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