Ali Mohammed
Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan.
Heliyon. 2021 Dec 23;7(12):e08626. doi: 10.1016/j.heliyon.2021.e08626. eCollection 2021 Dec.
In this article, appropriate sharp bounds for a certain class of rough maximal operators with mixed homogeneity are established. Specifically, when the function Ω belongs to with and , the boundedness of the such operators is obtained. Further, the extrapolation argument employed in [1] is applied on these gotten bounds to obtain the boundedness of the aforementioned operators whenever the kernels are in the space or in the block space with and . Our obtained results are considered substantial extensions and improvements of what was known previously.
在本文中，建立了一类具有混合齐次性的粗糙极大算子的适当精确界。具体而言，当函数Ω属于 且 时，得到了此类算子的有界性。此外，将[1]中使用的外推论证应用于这些得到的界，以在核属于空间 或属于块空间 且 时获得上述算子的有界性。我们得到的结果被认为是对先前已知结果的实质性扩展和改进。
