# A Multilier Theorem on Anisotropic Hardy Spaces

## TL;DR

This paper establishes a new multiplier theorem for anisotropic Hardy spaces, showing boundedness of certain operators under Mihlin conditions, extending classical results to anisotropic settings.

## Contribution

It introduces a multiplier theorem for anisotropic Hardy spaces, generalizing the classical Taibleson-Weiss theorem to anisotropic dilations and symbols.

## Key findings

- Boundedness of multiplier operators on anisotropic Hardy spaces.
- Extension of classical multiplier theorem to anisotropic settings.
- Dependence of boundedness on dilation eccentricities and symbol regularity.

## Abstract

We present a multiplier theorem on anisotropic Hardy spaces. When $m$ satisfies the anisotropic, pointwise Mihlin condition, we obtain boundedness of the multiplier operator $T_m : H_A^p (\mathbb{R}^n) \rightarrow H_A^p (\mathbb{R}^n)$, for the range of $p$ that depends on the eccentricities of the dilation $A$ and the level of regularity of a multiplier symbol $m$. This extends the classical multiplier theorem of Taibleson and Weiss.