Besov algebras on Lie groups of polynomial growth

TL;DR

This paper establishes that Besov spaces on Lie groups of polynomial growth form algebras under pointwise multiplication, and extends these results to paraproduct estimates specifically for H-type groups.

Contribution

It proves algebra properties for Besov spaces on polynomial growth Lie groups and generalizes to paraproduct estimates on H-type groups.

Findings

Besov spaces form algebras under pointwise multiplication on polynomial growth Lie groups.

Extension of algebra property to paraproduct estimates on H-type groups.

Provides foundational results for analysis on Lie groups with polynomial growth.

Abstract

We prove an algebra property under pointwise multiplication for Besov spaces defined on Lie groups of polynomial growth. When the setting is restricted to the case of H-type groups, this algebra property is generalized to paraproduct estimates.