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- W1992473338 abstract "It is shown that for 1 < p1, p2 < 1, 1/p3 = 1/p1 + 1/p2, p3 ≥ 1 there existsC 1 (independent ofn) such that $$left| {R_k (f,g)} right|_{L^{p_3 } (mathbb{R}^n )} leqslant C_1 left| f right|_{L^{p_1 } (mathbb{R}^n )} left| g right|_{L^{p_2 } (mathbb{R}^n )} $$ where $$R_k (f, g)(x) = b_n mathop {lim }limits_{varepsilon to 0} int_{left| y right| > varepsilon } { f} (x - y)g(x + y)frac{{y_k }}{{left| y right|^{n + 1} }}dy,$$ andb n is chosen so thatR k has norm 1 as a bilinear map fromL 2(ℝn) ×L 2(ℝn) →L 1(ℝn). In the casep 3 > 1 it is even shown that $$left| {left( {sumlimits_{k = 1}^n {left| {R_k (f, g)} right|^2 } } right)^{1/2} } right|_{L^{p_3 } (mathbb{R}^n )} leqslant C_2 left| f right|_{L^{p_1 } (mathbb{R}^n )} left| g right|_{L^{p_2 } (mathbb{R}^n )} $$ for some constantC 2 independent of the dimension." @default.
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- W1992473338 date "2009-10-01" @default.
- W1992473338 modified "2023-09-25" @default.
- W1992473338 title "Dimension free estimates for the bilinear Riesz transform" @default.
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- W1992473338 doi "https://doi.org/10.1007/bf03191370" @default.
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