混合模空间中的q-光滑模与Hardy-Littlewood型定理  

q-moduli of Smoothness and Hardy-Littlewood Type Theorem in Mixed Norm Spaces

作　　者：贾敏 陈英伟[1] JIA Min;CHEN Yingwei(College of Mathematics and Statistics,Hebei University of Economics and Business,Hebei Shijiazhuang 050061,China)

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061

出　　处：《河北师范大学学报（自然科学版）》2022年第1期17-26,共10页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11801132);河北省教育厅科技重点项目(ZD2020109)。

摘　　要：研究了混合模空间中全纯函数的逼近性质与其边界函数值的光滑性的密切关系.采用q-光滑模得出Jackson定理、q-光滑模与本性K-泛函的等价性,并在混合模空间中借助K-泛函获得关于导数增长的Hardy-Littlewood定理和强逆估计.Some aspects of the interplay between approximation properties of holomorphic functions in mixed norm spaces and the smoothness of its boundary values are discussed.We obtain Jackson theorem and the equivalence of a special q-modulus of smoothness and an intrinsic K-functional.Further,a generalization of Hardy-Littlewood theorem on the growth of derivatives and strong converse estimates are deduced by using K-functional in mixed norm spaces.

关 键 词：混合模空间 q-光滑模 HARDY-LITTLEWOOD不等式 K-泛函 

分 类 号：O174.41[理学—数学]