Uniform Fourier Restriction Estimate for Simple Curves of Bounded Frequency

Key Points

• The aim is to establish a uniform Fourier restriction estimate for simple curves with bounded frequency.
• Proven a uniform Fourier restriction estimate over simple curves.
• Extended the last coordinate function to a holomorphic function of bounded frequency.
• Utilized a decomposition scheme for the analysis.
• Provided a uniform estimate applicable to the defined class of simple curves.
• Demonstrated the effectiveness of the extension to holomorphic functions.

Abstract