Certain Estimates of Oscillatory Integrals and Extrapolation

In this paper we study the boundedness properties of certain oscillatory integrals with polynomial phase. We obtain sharp estimates for these oscillatory integrals. By the virtue of these estimates and extrapolation we obtain Lp boundedness for these oscillatory integrals under rather weak size conditions on the kernel function.

Authors:

• Hussain Al-Qassem

Keywords:

• Fourier transform
• oscillatory integrals
• Orlicz spaces
• Block spaces
• Extrapolation
• Lp boundedness.

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