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arXiv · 2301.11906

A sufficient condition for Haar multipliers in Triebel-Lizorkin spaces

Gustavo Garrigós·Andreas Seeger·Tino Ullrich
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Abstract

We consider Haar multiplier operators $T_m$ acting on Sobolev spaces, and more generally Triebel-Lizorkin spaces $F^s_{p,q}(\mathbb{R})$, for indices in which the Haar system is not unconditional. When $m$ depends only on the Haar frequency, we give a sufficient condition for the boundedness of $T_m$ in $F^s_{p,q}$, in terms of the variation norms $\|m\|_{V_u}$, which is optimal in $u$ (up to endpoints) when $p, q> 1$.

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Gustavo Garrigós, Andreas Seeger, Tino Ullrich. 2023-01-27. A sufficient condition for Haar multipliers in Triebel-Lizorkin spaces. https://arxiv.org/abs/2301.11906

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