Multilinear analysis on metric spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2014-01-01 DOI:10.4064/DM497-0-1

L. Grafakos, Liguang Liu, Diego Maldonado, Dachun Yang

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引用次数: 53

Abstract

The multilinear Calderón–Zygmund theory is developed in the setting of RD-spaces which are spaces of homogeneous type equipped with measures satisfying a reverse doubling condition. The multiple-weight multilinear Calderón–Zygmund theory in this context is also developed in this work. The bilinear T1-theorems for Besov and Triebel–Lizorkin spaces in the full range of exponents are among the main results obtained. Multilinear vector-valued T1 type theorems on Lebesgue spaces, Besov spaces, and Triebel–Lizorkin spaces are also proved. Applications include the boundedness of paraproducts and bilinear multiplier operators on products of Besov and Triebel–Lizorkin spaces. Acknowledgements. Loukas Grafakos is supported by grant DMS 0900946 of the National Science Foundation of the USA. Liguang Liu is supported by the National Natural Science Foundation of China (grant No. 11101425). Diego Maldonado is supported by grant DMS 0901587 of the National Science Foundation of the USA. Dachun Yang (the corresponding author) is supported by the National Natural Science Foundation of China (grant nos. 11171027 & 11361020) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (grant No. 20120003110003). All authors would like to thank the copy editor, Jerzy Trzeciak, for his valuable remarks which made this article more readable. 2010 Mathematics Subject Classification: Primary 42B20, 42B25, 42B35; Secondary 35S50, 42C15, 47G30, 30L99.

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度量空间的多线性分析

在具有满足反向加倍条件的测度的齐次空间rd -空间中，建立了多元线性Calderón-Zygmund理论。在此背景下，本工作还发展了多重权重多元线性Calderón-Zygmund理论。得到了Besov和triiebel - lizorkin空间在全指数范围内的双线性t1定理。证明了Lebesgue空间、Besov空间和triiebel - lizorkin空间上的多线性向量值T1型定理。应用于Besov和triiebel - lizorkin空间乘积上的副积和双线性乘子算子的有界性。致谢Loukas Grafakos由美国国家科学基金会DMS 0900946基金资助。刘利光是国家自然科学基金(批准号:11101425)资助对象。Diego Maldonado由美国国家科学基金会DMS 0901587基金资助。杨大春(通讯作者)是国家自然科学基金(批准号:11171027和11361020)和高等学校博士点专项科研基金(批准号:20120003110003)的资助对象。所有作者都要感谢文字编辑Jerzy Trzeciak，他的宝贵意见使本文更具可读性。2010年数学学科分类:初级42B20、42B25、42B35;二级35S50、42C15、47G30、30L99。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.