Hölder-Zygmund平滑曲线类

IF 0.7 3区 数学 Q2 MATHEMATICS
A. Rainer
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引用次数: 0

摘要

.我们证明了一个在多个变量中的函数在局部Zyg-mund类Zm,1中,当且仅当它与每一条光滑曲线的组合为Zm,1。这补充了我们在此过程中对局部H¨older–Lipschitz类C m,α的众所周知的类似结果。我们证明了这些结果推广到Banach空间之间的映射,并用它们来研究叠加算子f*:g7的正则性→ f◦ g作用于Zygmund空间∧m+1(Rd)。我们证明了,对于所有整数m,k k,R)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hölder–Zygmund classes on smooth curves
. We prove that a function in several variables is in the local Zyg- mund class Z m, 1 if and only if its composite with every smooth curve is of class Z m, 1 . This complements the well-known analogous result for local H¨older– Lipschitz classes C m,α which we reprove along the way. We demonstrate that these results generalize to mappings between Banach spaces and use them to study the regularity of the superposition operator f ∗ : g 7→ f ◦ g acting on the Zygmund space Λ m +1 ( R d ). We prove that, for all integers m,k k, R ).
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来源期刊
CiteScore
1.80
自引率
0.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.
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