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- W1574351208 abstract "We prove that the degenerate trilinear operator $C_3^{-1,1,1}$ given by the formula begin{eqnarray*} C_3^{-1,1,1}(f_1, f_2, f_3)(x)=int_{x_1 < x_2 < x_3} hat{f}_1(x_1) hat{f}_2(x_2) hat{f}_3(x_3) e^{2pi i x (-x_1 + x_2 + x_3)} dx_1dx_2 dx_3 end{eqnarray*} satisfies the estimate begin{eqnarray*} ||C_3^{-1,1,1}(vec{f})||_{frac{1}{frac{1}{p_1}+frac{1}{p_2}+frac{1}{p_3}}} lesssim_{p_1, p_2, p_3} ||hat{f}_1||_{p^prime_1} ||f_2||_{p_2}||f_3||_{p_3} end{eqnarray*} for all $f_1 in L^{p_1}(mathbb{R}): hat{f}_1 in L^{p_1^prime}(mathbb{R}) , f_2 in L^{p_2}(mathbb{R})$, and $f_3 in L^{p_3}(mathbb{R})$ under the assumption that $p_1 >2, frac{1}{p_1}+frac{1}{p_2} <1$, and $frac{1}{p_2}+frac{1}{p_3} <3/2$. Mixed estimates for some multilinear generalizations of $C_3^{-1,1,1}$ and for several tensor product operators such as $BHT otimes BHT$ are also shown. As an application, we obtain the boundedness of special upper-triangular biparameter AKNS systems." @default.
- W1574351208 created "2016-06-24" @default.
- W1574351208 creator A5024538360 @default.
- W1574351208 date "2013-11-11" @default.
- W1574351208 modified "2023-09-27" @default.
- W1574351208 title "Mixed Estimates for Degenerate Multilinear Oscillatory Integrals and their Tensor Product Generalizations" @default.
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