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

TL;DR

This paper investigates Besov spaces of analytic type on the boundary of Siegel domains, exploring their properties, relationships with classical Besov spaces, and their behavior under convolution, Fourier multipliers, and interpolation.

Contribution

It introduces a detailed analysis of Besov spaces of analytic type on Siegel domain boundaries and compares them with classical Besov spaces, expanding understanding of their functional properties.

Findings

Characterization of Besov spaces of analytic type

Relations between analytic and classical Besov spaces

Results on convolution and Fourier multipliers

Abstract

We consider a family of Besov spaces of analytic type on the Shilov boundary $\mathcal{N}$ of a homogeneous Siegel domain $D$, and study their properties in relation to convolution, Fourier multipliers, and complex interpolation. In addition, we study how these Besov spaces of analytic type can be compared with the `classical' Besov spaces $\mathcal{N}$.