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- W2810146333 abstract "We complete our boundedness theory of commutators of bilinear bi-parameter singular integrals by establishing the following result. If $T$ is a bilinear bi-parameter singular integral satisfying suitable $T1$ type assumptions, $|b|_{operatorname{bmo}(mathbb{R}^{n+m})} = 1$ and $1 < p, q le infty$ and $1/2 < r < infty$ satisfy $1/p+1/q = 1/r$, then we have $$ |[b, T]_1(f_1, f_2)|_{L^r(mathbb{R}^{n+m})} lesssim |f_1|_{L^p(mathbb{R}^{n+m})} |f_2|_{L^q(mathbb{R}^{n+m})}. $$ Previously the range $r le 1$ was proved only in the paraproduct free situation. The main novelty lies in the treatment of the so called partial paraproducts." @default.
- W2810146333 created "2018-07-10" @default.
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- W2810146333 date "2018-06-25" @default.
- W2810146333 modified "2023-09-27" @default.
- W2810146333 title "Quasi-Banach estimates of commutators of bilinear bi-parameter singular integrals: paraproducts" @default.
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