# Characteristic functions as bounded multipliers on anisotropic spaces

## TL;DR

This paper proves that characteristic functions of certain domains act as bounded multipliers on specific anisotropic Banach spaces, under particular geometric and parameter conditions, advancing the understanding of functional analysis in anisotropic settings.

## Contribution

It establishes the boundedness of characteristic functions as multipliers on the $U^{t,s}_p$ anisotropic spaces for domains with boundaries transversal to stable cones, under new parameter conditions.

## Key findings

- Characteristic functions are bounded multipliers on $U^{t,s}_p$ spaces.
- Results depend on boundary transversality and parameter constraints.
- Advances the theory of multipliers in anisotropic Banach spaces.

## Abstract

We show that characteristic functions of domains with boundaries transversal to stable cones are bounded multipliers on a recently introduced scale $U^{t,s}_p$ of anisotropic Banach spaces, under the conditions -1+1/p<s<-t<0 and -(r-1)+t<s, with 1<p<infty. (Amended after comments from the referee and M. J\'ez\'equel, January 10, 2018)