TY - JOUR
T1 - Bilinear oscillatory integrals and boundedness for new bilinear multipliers
AU - Bernicot, Frédéric
AU - Germain, Pierre
PY - 2010/11
Y1 - 2010/11
N2 - We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger; this extends the well-known linear theory of oscillatory integral in some directions. The proof relies on a combination of time-frequency analysis of Coifman-Meyer type with stationary and non-stationary phase estimates. As a consequence of this analysis, we obtain Lebesgue estimates for new bilinear multipliers defined by non-smooth symbols.
AB - We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger; this extends the well-known linear theory of oscillatory integral in some directions. The proof relies on a combination of time-frequency analysis of Coifman-Meyer type with stationary and non-stationary phase estimates. As a consequence of this analysis, we obtain Lebesgue estimates for new bilinear multipliers defined by non-smooth symbols.
KW - Bilinear multipliers
KW - Oscillatory integrals
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U2 - 10.1016/j.aim.2010.03.032
DO - 10.1016/j.aim.2010.03.032
M3 - Article
AN - SCOPUS:77956232653
SN - 0001-8708
VL - 225
SP - 1739
EP - 1785
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 4
ER -