Abstract
In this paper, we consider a model of degenerate and singular oscillatory integral operators in which the phase functions are homogeneous polynomials of degree n and the singular kernel K(x, y) satisfies suitable conditions related to a real parameter μ. We show that the sharp decay estimates on L2 spaces, obtained in the previous work, can be preserved on more general Lp spaces with an additional condition imposed on the singular kernel. Moreover, the case without the additional condition is also discussed.
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Acknowledgements
The author would like to acknowledge financial support from Jiangsu Natural Science Foundation (No. BK20200308). The author thanks Zuoshunhua Shi for many helpful suggestions and expresses gratitude to the referees for their careful reading and valuable suggestions.
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Xu, S. Sharp Lp Decay Estimates for Degenerate and Singular Oscillatory Integral Operators. Front. Math 18, 615–638 (2023). https://doi.org/10.1007/s11464-021-0235-z
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DOI: https://doi.org/10.1007/s11464-021-0235-z