Bilinear oscillatory integrals and boundedness for new bilinear multipliers
Copyright policy )Bilinear oscillatory integrals and boundedness for new bilinear multipliers
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.
35 pages, 3 figures
- French National Centre for Scientific Research France
- university of lille France
- New York University United States
- University of Lille France
- Laboratoire Paul Painlevé France
bilinear multipliers, Mathematics(all), Singular and oscillatory integrals (Calderón-Zygmund, etc.), Bilinear multipliers, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], Mathematics - Analysis of PDEs, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 42B10, Oscillatory integrals, pseudo-products, oscillatory integrals, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 42B20, 42B10 ; 42B20, Bilinear operators, Analysis of PDEs (math.AP)
bilinear multipliers, Mathematics(all), Singular and oscillatory integrals (Calderón-Zygmund, etc.), Bilinear multipliers, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], Mathematics - Analysis of PDEs, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 42B10, Oscillatory integrals, pseudo-products, oscillatory integrals, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 42B20, 42B10 ; 42B20, Bilinear operators, Analysis of PDEs (math.AP)
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