Li Bo, Liao Minfeng, Li Baode
College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046 P.R. China.
J Inequal Appl. 2017;2017(1):228. doi: 10.1186/s13660-017-1501-1. Epub 2017 Sep 19.
Let [Formula: see text] satisfy that [Formula: see text], for any given [Formula: see text], is an Orlicz function and [Formula: see text] is a Muckenhoupt [Formula: see text] weight uniformly in [Formula: see text]. The Musielak-Orlicz Hardy space [Formula: see text] is defined to be the set of all tempered distributions such that their grand maximal functions belong to the Musielak-Orlicz space [Formula: see text]. In this paper, the authors establish the boundedness of Marcinkiewicz integral [Formula: see text] from [Formula: see text] to [Formula: see text] under weaker smoothness conditions assumed on Ω. This result is also new even when [Formula: see text] for all [Formula: see text], where is an Orlicz function.
设([公式：见正文])满足，对于任意给定的([公式：见正文])，是一个奥利奇函数且([公式：见正文])是一个在([公式：见正文])中一致的穆肯霍普特([公式：见正文])权。穆西亚拉克 - 奥利奇函数哈代空间([公式：见正文])被定义为所有缓增广义函数的集合，使得它们的极大函数属于穆西亚拉克 - 奥利奇空间([公式：见正文])。在本文中，作者在对(\Omega)假设的较弱光滑性条件下，建立了马尔钦凯维奇积分([公式：见正文])从([公式：见正文])到([公式：见正文])的有界性。即使对于所有([公式：见正文])，当([公式：见正文])（其中([公式：见正文])是一个奥利奇函数）时，该结果也是新的。
