In their work Ikromov and Müller (Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra. Princeton University Press, Princeton, 2016) proved the full range $$L^p-L^2$$ L p - L 2 Fourier restriction estimates for a very general class of hypersurfaces in $${\mathbb {R}}^3$$ R 3 which includes the class of real analytic hypersurfaces. In this article we partly extend their results to the mixed norm case where the coordinates are split in two directions, one tangential and the other normal to the surface at a fixed given point. In particular, we resolve completely the adapted case and partly the non-adapted case. In the non-adapted case the case when the linear height $$h_\text {lin}(\phi )$$ h lin ( ϕ ) is below two is settled completely.

中文翻译：

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三维超曲面的混合范数 Strichartz 型估计

在他们的工作 Ikromov 和 Müller（Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra。Princeton University Press, Princeton, 2016）证明了全范围 $$L^pL^2$$ L p - L 2 傅里叶限制估计$${\mathbb {R}}^3$$ R 3 中的超曲面的一般类，其中包括实解析超曲面的类。在本文中，我们将他们的结果部分扩展到混合范数情况，其中坐标在两个方向上分开，一个是切线，另一个是在固定给定点的表面法线。特别是，我们完全解决了适应情况和部分非适应情况。在非适应情况下，当线性高度 $$h_\text {lin}(\phi )$$h lin ( ϕ ) 低于 2 时完全解决。