The boundedness from Hp×L2\documentclass[12pt]{minimal}
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\begin{document}$$H^p \times L^2$$\end{document} to Lr\documentclass[12pt]{minimal}
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\begin{document}$$L^r$$\end{document}, 1/p+1/2=1/r\documentclass[12pt]{minimal}
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\begin{document}$$1/p+1/2=1/r$$\end{document}, and from Hp×L∞\documentclass[12pt]{minimal}
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\begin{document}$$H^p \times L^{\infty }$$\end{document} to Lp\documentclass[12pt]{minimal}
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\begin{document}$$L^p$$\end{document} of bilinear pseudo-differential operators is proved under the assumption that their symbols are in the bilinear Hörmander class BSρ,ρm\documentclass[12pt]{minimal}
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\begin{document}$$BS^m_{\rho ,\rho }$$\end{document}, 0≤ρ<1\documentclass[12pt]{minimal}
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\begin{document}$$0 \le \rho <1$$\end{document}, of critical order m, where Hp\documentclass[12pt]{minimal}
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\begin{document}$$H^p$$\end{document} is the Hardy space. This combined with the previous results of the same authors establishes the sharp boundedness from Hp×Hq\documentclass[12pt]{minimal}
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\begin{document}$$H^p \times H^q$$\end{document} to Lr\documentclass[12pt]{minimal}
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\begin{document}$$L^r$$\end{document}, 1/p+1/q=1/r\documentclass[12pt]{minimal}
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\begin{document}$$1/p+1/q=1/r$$\end{document}, of those operators in the full range 0<p,q≤∞\documentclass[12pt]{minimal}
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\begin{document}$$0< p, q \le \infty $$\end{document}, where Lr\documentclass[12pt]{minimal}
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\begin{document}$$L^r$$\end{document} is replaced by BMO if r=∞\documentclass[12pt]{minimal}
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\begin{document}$$r=\infty $$\end{document}.