混合范数Herz空间及其在相关Hardy空间中的应用

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Yirui Zhao, Dachun Yang, Yangyang Zhang
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引用次数: 10

摘要

本文引入了一类混合范数Herz空间[公式:见文],它是混合范数Lebesgue空间的自然推广,并且在研究混合范数Lebesgue空间上傅里叶变换的可和性时自然出现了一些特殊的情况。给出了它们的对偶空间,并在[公式:见文]上得到了Riesz-Thorin插值定理。利用这些Riesz-Thorin插值定理和外推定理中的一些思想,在[公式:见文]上建立了Hardy-Littlewood极大算子和Fefferman-Stein向量值极大不等式的有界性。作为应用,作者利用与球拟巴拿赫函数空间相关的Hardy空间的已有结果,发展了与[公式:见文]相关的Hardy空间的各种实变量理论。这些结果强烈依赖于[公式:见文本]的对偶性和Riesz-Thorin插值定理中辅助函数的非平凡构造。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mixed-norm Herz spaces and their applications in related Hardy spaces
In this paper, the authors introduce a class of mixed-norm Herz spaces, [Formula: see text], which is a natural generalization of mixed-norm Lebesgue spaces and some special cases of which naturally appear in the study of the summability of Fourier transforms on mixed-norm Lebesgue spaces. The authors also give their dual spaces and obtain the Riesz–Thorin interpolation theorem on [Formula: see text]. Applying these Riesz–Thorin interpolation theorem and using some ideas from the extrapolation theorem, the authors establish both the boundedness of the Hardy–Littlewood maximal operator and the Fefferman–Stein vector-valued maximal inequality on [Formula: see text]. As applications, the authors develop various real-variable theory of Hardy spaces associated with [Formula: see text] by using the existing results of Hardy spaces associated with ball quasi-Banach function spaces. These results strongly depend on the duality of [Formula: see text] and the non-trivial constructions of auxiliary functions in the Riesz–Thorin interpolation theorem.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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