2022/04/24 by T. Godoy, Godoy, Tomás, Pablo Rocha +1
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2204.11347
openalex publication_date 2022/04/24 · openalex created_date 2022/04/28 · openalex updated_date 2026/07/28
We consider, for a class of functions φ: ℝ2 ∖ \ \bf 0 \ → ℝ2 satisfying a nonisotropic homogeneity condition, the Fourier transform μ of the Borel measure on ℝ4 defined by μ(E) = ∫U χE(x, φ(x)) dx where E is a Borel set of ℝ4 and U = \ (tα1, tα2s) : c < s < d, 0 < t < 1 \. The aim of this article is to give a decay estimate for μ, for the case where the set of nonelliptic points of φ is a curve in U ∖ \ \bf 0 \. From this estimate we obtain a restriction theorem for the usual Fourier transform to the graph of φU : U → ℝ2. We also give Lp-improving properties for the convolution operator Tμ f = μ∗ f.