Mathematical Sciences: NSF-CBMS Regional Conference on New Function Spaces and Geometric Analysis in Several Complex Variables to be held in Fairfax, VA May 26-31, 1992

在许多意义上，欧氏空间的调和分析已经得到了很好的发展。对分数次积分、奇异积分、常系数偏微分算子的参数及相关问题有很好的了解。在所有这些理论中，翻译不变性起着至关重要的作用。特别是，傅立叶分析是所有这些工作的中心工具。许多物理问题--气体绕过障碍物的流动、湍流、流量问题、Dirichlet和Neumann问题等--都有一个光滑有界的区域作为它们的自然设置(其中所需的平滑程度可能会随着应用的不同而变化)。调和分析和复变函数论的许多基本问题的正则设置也是空间中的一个领域。因此，开发针对域的几何形状定制的分析工具变得合适。这导致了重新考虑这些区域上的经典函数空间，并使用不变度量来研究它们。该项目将支持将于1992年5月26日至31日在乔治梅森大学举行的NSF-CBMS关于新函数空间和几个复变量中的几何分析的数学科学区域研究会议。华盛顿大学的史蒂文·克兰茨教授将担任首席讲师。为了激发人们对数学研究的兴趣和活力，美国国家科学基金会每年都会支持一些NSF-CBMS数学科学区域研究会议。每个为期五天的会议都有一位杰出的讲师，他就一个重要的当前研究主题发表十次演讲，该主题是数学科学中一个尖锐的重点领域。讲师随后根据这些讲座编写一份说明性专著，通常由美国数学学会或工业和应用数学学会出版，或由美国统计协会和数学统计研究所联合出版。这些会议的某些特点使其有别于典型的研究会议。它们是：(1)由领先的实践者专注于一个重要和及时的研究领域，(2)通过区域重点来持续影响和局部刺激，(3)小组审查质量、广度和及时性，以及(4)出版面向更广泛受众的专著。

In many senses the harmonic analysis of Euclidean space is well developed. The theories of fractional integration, singular integrals, parametrices for constant coefficient partial differential operators, and related matters are well understood. In all of these theories, translation invariance plays a crucial role. In particular, Fourier analysis is a central tool in all of this work. Many physical problems - the flow of gas around an obstacle, turbulence, problems of flux, Dirichlet and Neumann problems, etc. - have as their natural setting a smoothly bounded domain (where the necessary degree of smoothness may vary with the application). The canonical setting for many of the basic problems of harmonic analysis and of complex function theory is also a domain in space. Thus, it becomes appropriate to develop analytic tools tailored to the geometry of domains. This leads to reconsidering classical function spaces on these domains and to studying them with the use of invariant metrics. This project will support an NSF-CBMS Regional Research Conference in the Mathematical Sciences on New Function Spaces and Geometric Analysis in Several Complex Variables to be held May 26-31, 1992 at George Mason University. Professor Steven Krantz of Washington University will be the principal lecturer. To stimulate interest and activity in mathematical research, the National Science Foundation each year supports a number of NSF- CBMS Regional Research Conferences in the Mathematical Sciences. Each five-day conference features a distinguished lecturer who delivers ten lectures on a topic of important current research in one sharply focused area of the mathematical sciences. The lecturer subsequently prepares an expository monograph based upon these lectures, which is normally published by the American Mathematical Society or the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Institute of Mathematical Statistics. Certain features differentiate these conferences from typical research conferences. These are: (1) Focus on a single important and timely area of research by a leading practitioner, (2) Continued effect and local stimulation through regional emphasis, (3) Panel review for quality, breadth, and timeliness, and (4) Published monographs for a wider audience.