Littlewood–Paley and Finite Atomic Characterizations of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications
Littlewood–Paley and Finite Atomic Characterizations of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications
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DOI：
10.1007/s00041-018-9609-3
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发表时间：
2018-04
影响因子：
1.2
通讯作者：
Jun Liu;F. Weisz;Dachun Yang;Wen Yuan
中科院分区：
文献类型：
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作者：
Jun Liu;F. Weisz;Dachun Yang;Wen Yuan
设A是一个满足全局log-Hölder连续条件的变指数函数，A是上的一般扩张矩阵，A是由径向极大函数定义的各向异性变Hardy-Lorentz空间.本文首先在变Lorentz空间上建立了一个各向异性的Fittleman-Stein向量值不等式，然后利用Littlewood-Paleyg函数或Littlewood-Paley函数刻画了变Lorentz空间上的Fittleman-Stein向量值不等式.此外，还得到了的有限原子特征.作为应用，建立了从~到拟Banach空间的次线性算子有界性的一个判别准则.应用这个准则，证明了Bochner-Riesz平均和Weierstrass平均的极大算子是有界的，并由此得到了Bochner-Riesz平均和Weierstrass平均的几乎处处收敛性和范数收敛性.这些结果的Bochner-Riesz和Weierstrass手段是新的，即使在各向同性的情况下。
Letbe a variable exponent function satisfying the globally log-Hölder continuous condition,andAbe a general expansive matrix on. Letbe the anisotropic variable Hardy–Lorentz space associated withAdefined via the radial grand maximal function. In this article, the authors characterizeby means of the Littlewood–Paleyg-function or the Littlewood–Paley-function via first establishing an anisotropic Fefferman–Stein vector-valued inequality on the variable Lorentz space. Moreover, the finite atomic characterization ofis also obtained. As applications, the authors then establish a criterion on the boundedness of sublinear operators frominto a quasi-Banach space. Applying this criterion, the authors show that the maximal operators of the Bochner–Riesz and the Weierstrass means are bounded fromtoand, as consequences, some almost everywhere and norm convergences of these Bochner–Riesz and Weierstrass means are also obtained. These results on the Bochner–Riesz and the Weierstrass means are new even in the isotropic case.