Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved bound for the bilinear Bochner-Riesz operator   We study $L^p\times L^q\to L^r$ bounds for the bilinear Bochner-Riesz
operator $\mathcal{B}^\alpha$, $\alpha>0$ in $\mathbb{R}^d,$ $d\ge2$, which is
defined by \[ {\mathcal B}^{\alpha}(f,g)=\iint_{\mathbb{R}^d\times\mathbb{R}^d}
e^{2\pi i x\cdot(\xi+\eta)} (1-|\xi|^2-|\eta|^2 )^{\alpha}_+ ~
\widehat{f}(\xi)\,\widehat{g}(\eta)\,d\xi d\eta.\] We make use of a
decomposition which relates the estimates for $\mathcal{B}^\alpha$ to those of
the square function estimates for the classical Bochner-Riesz operators. In
consequence, we significantly improve the previously known bounds.

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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: stat