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- W4287912310 abstract "Let $mathscr{R}$ be a collection of disjoint dyadic rectangles $R$ with sides parallel to the axes, let $pi_R$ denote the non-smooth bilinear projection onto $R$ [ pi_R (f,g)(x):=iint mathbf{1}_{R}(xi,eta) widehat{f}(xi) widehat{g}(eta) e^{2pi i (xi + eta) x} dxi deta ] and let $r>2$. We show that the bilinear Rubio de Francia operator associated to $mathscr{R}$ given by [ f,g mapsto Big(sum_{Rinmathscr{R}} |pi_{R} (f,g)|^r Big)^{1/r} ] is $L^p times L^q rightarrow L^s$ bounded whenever $1/p + 1/q = 1/s$, $r'<p,q<r$. This extends from squares to rectangles a previous result by the same authors, and as a corollary extends in the same way a previous result from Benea and the first author for smooth projections, albeit in a reduced range." @default.
- W4287912310 created "2022-07-26" @default.
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- W4287912310 date "2020-01-01" @default.
- W4287912310 modified "2023-10-03" @default.
- W4287912310 title "A bilinear Rubio de Francia inequality for arbitrary rectangles" @default.
- W4287912310 hasPublicationYear "2020" @default.
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