Truncated smooth function spaces

TL;DR

This paper introduces truncated Besov and Triebel–Lizorkin function spaces, exploring their properties to enhance results in functional analysis and PDEs.

Contribution

It presents new truncated function spaces and studies their key properties, improving existing theoretical results in analysis and partial differential equations.

Findings

Established embeddings, interpolation, duality, lifting, and trace properties of the new spaces.

Improved known results in functional analysis and PDEs using these truncated spaces.

Provided a framework for further research in analysis and PDE applications.

Abstract

We introduce truncated Besov and Triebel--Lizorkin function spaces and investigate their main properties: embeddings, interpolation, duality, lifting, traces. These new scales allow us to improve several known results in functional analysis and PDE's.