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• W2780217641 abstract "Our setup is a natural class of operators $T$, which we think of as general (not necessarily of tensor product or convolution type) bilinear bi-parameter singular integrals on the product space $mathbb{R}^{n+m} = mathbb{R}^n times mathbb{R}^m$. Starting from $T1$ type assumptions, we show a representation theorem for these operators using dyadic model operators. For singular integrals that are free of full paraproducts we use the representation to show weighted estimates $L^p(w_1) times L^q(w_2) to L^r(v_3)$, where $1 < p, q < infty$, $1/2 < r < infty$, $1/p+1/q = 1/r$, $w_1 in A_p(mathbb{R}^n times mathbb{R}^m)$, $w_2 in A_q(mathbb{R}^n times mathbb{R}^m)$ and $v_3 := w_1^{r/p} w_2^{r/q}$. We also consider mixed-norm estimates. Somewhat weaker unweighted estimates are obtained for all singular integrals. As an application we give a new proof of a result of Muscalu-Pipher-Tao-Thiele: a bi-parameter version of the bilinear multiplier theorem of Coifman and Meyer. In fact, we prove a weighted version of the result, and recover, apart from some $L^{infty}$ endpoints, the full range of mixed-norm estimates proved by Benea-Muscalu." @default.
• W2780217641 created "2018-01-05" @default.
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• W2780217641 date "2017-12-21" @default.
• W2780217641 modified "2023-09-27" @default.
• W2780217641 title "Bilinear bi-parameter singular integrals: Representation theorem and boundedness properties" @default.
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