Pointwise Multiplication by the Characteristic Function of the Half-space on Anisotropic Vector-valued Function Spaces

TL;DR

This paper investigates the conditions under which the characteristic function of a half-space acts as a pointwise multiplier on complex anisotropic vector-valued function spaces, extending understanding in functional analysis.

Contribution

It provides new insights into the multiplier properties of characteristic functions on weighted mixed-norm anisotropic vector-valued spaces, specifically for Bessel potential and Triebel-Lizorkin types.

Findings

Characterizes when the characteristic function is a pointwise multiplier

Extends multiplier theory to anisotropic vector-valued function spaces

Provides conditions for boundedness on weighted mixed-norm spaces

Abstract

We study the pointwise multiplier property of the characteristic function of the half-space on weighted mixed-norm anisotropic vector-valued function spaces of Bessel potential and Triebel-Lizorkin type.