论文标题
伪型伪造者和在Hermite besov和Hermite Triebel- -lizorkin空间上的平滑分子
Pseudo-multipliers and smooth molecules on Hermite Besov and Hermite Triebel--Lizorkin spaces
论文作者
论文摘要
我们获得了Hermite Besov和Hermite Triebel--Lizorkin空间的新分子分解和分子合成估计，并使用此类工具在这些空间上证明Hermite Pseudo-Multipliers的界限。我们开发的分子概念导致伪型型与Hörmander-type符号相关的伪型界面，该符号适用于具有非阳性平滑度的空间上的Hermite设置。特别是，我们为Lebesgue和Hermite当地Hardy空间上的此类运营商获得了连续性结果。作为我们对伪型伪造者的界限性能的副产品，我们表明Hermite besov空间和Hermite Triebel--lizorkin空间在非线性下封闭。
We obtain new molecular decompositions and molecular synthesis estimates for Hermite Besov and Hermite Triebel--Lizorkin spaces and use such tools to prove boundedness properties of Hermite pseudo-multipliers on those spaces. The notion of molecule we develop leads to boundedness of pseudo-multipliers associated to symbols of Hörmander-type adapted to the Hermite setting on spaces with non-positive smoothness; in particular, we obtain continuity results for such operators on Lebesgue and Hermite local Hardy spaces. As a byproduct of our results on boundedness properties of pseudo-multipliers, we show that Hermite Besov spaces and Hermite Triebel--Lizorkin spaces are closed under non-linearities.
