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

UR - http://www.scopus.com/inward/record.url?scp=77956232653&partnerID=8YFLogxK

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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

VL - 225

SP - 1739

EP - 1785

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 4

ER -