# Improved bound for the bilinear Bochner–Riesz operator

Improved bound for the bilinear Bochner–Riesz operator We study $$L^p\times L^q\rightarrow L^r$$ L p × L q → L r bounds for the bilinear Bochner–Riesz operator $$\mathcal {B}^\alpha$$ B α , $$\alpha >0$$ α > 0 in $${\mathbb {R}}^d,$$ R d , $$d\ge 2$$ d ≥ 2 , which is defined by [Equation not available: see fulltext.]We make use of a decomposition which relates the estimates for $$\mathcal {B}^\alpha$$ B α to the square function estimates for the classical Bochner–Riesz operators. In consequence, we significantly improve the previously known bounds. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Annalen Springer Journals

# Improved bound for the bilinear Bochner–Riesz operator

Mathematische Annalen, Volume 372 (2) – May 30, 2018
29 pages

/lp/springer-journals/improved-bound-for-the-bilinear-bochner-riesz-operator-TaZzr3Kblc
Publisher
Springer Journals
Subject
Mathematics; Mathematics, general
ISSN
0025-5831
eISSN
1432-1807
DOI
10.1007/s00208-018-1696-6
Publisher site
See Article on Publisher Site

### Abstract

We study $$L^p\times L^q\rightarrow L^r$$ L p × L q → L r bounds for the bilinear Bochner–Riesz operator $$\mathcal {B}^\alpha$$ B α , $$\alpha >0$$ α > 0 in $${\mathbb {R}}^d,$$ R d , $$d\ge 2$$ d ≥ 2 , which is defined by [Equation not available: see fulltext.]We make use of a decomposition which relates the estimates for $$\mathcal {B}^\alpha$$ B α to the square function estimates for the classical Bochner–Riesz operators. In consequence, we significantly improve the previously known bounds.

### Journal

Mathematische AnnalenSpringer Journals

Published: May 30, 2018

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