Uniform Convolution and Fourier Restriction estimates for complex polynomial curves in $\mathbb{C}^3$

Uniform Fourier Restriction Estimate for Simple Curves of Bounded Frequency

In this paper we prove a uniform Fourier restriction estimate over the class of simple curves where the last coordinate function can be extended to a holomorphic function of bounded frequency in a sufficiently large disc. The proof is based on a decomposition scheme for this class of functions.

Circle embeddings with restrictions on Fourier coefficients

This paper continues the investigation of the relation between the geometry of a circle embedding and the values of its Fourier coefficients. First, we answer a question of Kovalev and Yang concerning the support of the Fourier transform of a starlike embedding. An important special case of circle embeddings are homeomorphisms of the circle onto itself. Under a one-sided bound on the Fourier support, such homeomorphisms are rational functions related to Blaschke products. We study the structure of rational circle homeomorphisms and show that they form a connected set in the uniform topology.

Slice Fourier transform and convolutions

Recently the construction of various integral transforms for slice monogenic functions has gained a lot of attention. In line with these developments, the article at hand introduces the slice Fourier transform. In the first part, the kernel function of this integral transform is constructed using the Mehler formula. An explicit expression for the integral transform is obtained and allows for the study of its properties. In the second part, two kinds of corresponding convolutions are examined: Mustard convolutions and convolutions based on generalised translation operators. The paper finishes b…

解析型 Besov 空间：插值、卷积、Fourier 乘子与包含关系

Besov Spaces of Analytic Type: Interpolation, Convolution, Fourier Multipliers, Inclusions

本文研究齐次 Siegel 域 Shilov 边界上的解析型 Besov 空间，分析其卷积、Fourier 乘子、复插值性质，并比较其与经典 Besov 空间的关系。