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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.
Mathematische Annalen – Springer Journals
Published: May 30, 2018
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