A decay estimate for the Fourier transform of certain singular measures in \(\mathbb{R}^4\) and applications (Q6111821)

The authors consider the restriction operators and give a decay estimate for the Fourier transform \(\mu\) of the Borel measure on \(R^4\) for the case where the set of nonelliptic points of a function \(\phi\), satisfying a nonisotropic homogeneity condition, is an opportune curve.\par From this estimate, the authors obtain a restriction theorem for the usual Fourier transform to the graph of a suitable restriction of \(\phi.\) \par In addition, Godoy and Rocha prove \(L^p\)-improving properties for some convolution operators.