Kernel theorems for Beurling-Bj\"orck type spaces

TL;DR

This paper establishes new kernel theorems for a broad class of Beurling-Björck type spaces, extending classical results to spaces defined by weight functions, which enhances understanding of their structure and applications.

Contribution

It introduces generalized kernel theorems applicable to a wide range of Beurling-Björck spaces, including classical variants defined by weight functions.

Findings

Proved kernel theorems for generalized Beurling-Björck spaces

Extended classical results to spaces with weight functions

Provided a unified framework for these function spaces

Abstract

We prove new kernel theorems for a general class of Beurling-Bj\"orck type spaces. In particular, our results cover the classical Beurling-Bj\"orck spaces $\mathcal{S}^{(\omega)}_{(\eta)}$ and $\mathcal{S}^{\{\omega\}}_{\{\eta\}}$ defined via weight functions $\omega$ and $\eta$.