Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2020-07-25 , DOI: 10.1016/j.jat.2020.105459 Long Huang , Jun Liu , Dachun Yang , Wen Yuan
Let be the Schwartz class on and and and be their dual spaces, respectively. Let , , and be the anisotropic mixed-norm Hardy space, associated with an anisotropic quasi-homogeneous norm , defined via the non-tangential grand maximal function. In this article, via the known atomic characterizations and Lusin area function characterizations of , the authors first establish a new atomic characterization of in terms of . Applying this atomic characterization, the authors then obtain the Littlewood–Paley -function characterization of in terms of , which further induces the identification of and certain anisotropic homogeneous mixed-norm Triebel–Lizorkin spaces. As applications, the authors obtain the dual theorem on some anisotropic homogeneous mixed-norm Triebel–Lizorkin spaces and the boundedness of Fourier multipliers as well as anisotropic pseudo-differential operators on . All these results are new even for isotropic mixed-norm Hardy spaces on .
中文翻译:
各向异性混合范数Hardy空间和某些齐次Triebel-Lizorkin空间的识别
让 成为施瓦茨课程 和 和 和 分别是它们的双重空间。让, 和 是各向异性混合范式Hardy空间,与各向异性拟齐范数相关 ,是通过非切线的Grand max函数定义的。在本文中,通过已知的原子表征和Lusin面函数表征,作者首先建立了一个新的原子表征 就......而言 。应用这种原子特性,作者便获得了Littlewood–Paley的功能表征 就......而言 ,这进一步导致了对 以及某些各向异性的齐次混合规范Triebel–Lizorkin空间。作为应用,作者获得了一些各向异性齐次混合范Triebel-Lizorkin空间上的对偶定理,以及Fourier乘子的有界性以及各向异性伪微分算子在。所有这些结果,即使对于上的各向同性混合范数Hardy空间,也是新的。