Sharp \(L^{p}\)-boundedness of oscillatory integral operators with polynomial phases. (English) Zbl 06780328
Summary: In this paper, we shall prove the \(L^{p}\) endpoint decay estimates of oscillatory integral operators with homogeneous polynomial phases \(S\) in \(\mathbb {R} \times \mathbb {R}\). As a consequence, sharp \(L^{p}\) decay estimates are also obtained when polynomial phases have the form \(S(x^{m_{1}},y^{m_{2}})\) with \(m_1\) and \(m_2\) being positive integers.
Keywords:
sharp \(L^p\) boundedness; oscillatory integral operators; polynomial phases; endpoint decay estimatesReferences:
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