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，欧几里得空间的调和分析是 发育良好。 分数阶积分、奇异积分 常系数偏微分方程的参数积分 微分算子和相关问题都很好理解。 在所有这些理论中，翻译不变性起着至关重要的作用。 作用 特别是，傅立叶分析是所有分析的核心工具。 这个工作。 许多物理问题-气体绕流 障碍，湍流，通量问题，Dirichlet和Neumann 问题，等等-作为他们的自然设置一个光滑的边界 域（其中必要的平滑度可能随 的应用）。 许多基本的 调和分析和复变函数论的问题， 也是太空中的一个领域。 因此，开发 为域的几何形状量身定制的分析工具。 这导致 重新考虑这些域上的经典函数空间， to studying研究them with the use of invariant不变metrics度量. 该项目将支持NSF-CBMS区域研究 新函数空间数学科学会议 和几何分析在几个复杂的变量举行 1992年5月26日至31日在乔治梅森大学。 史提芬教授 华盛顿大学的“将军”将担任首席讲师。 为了激发数学研究的兴趣和积极性， 美国国家科学基金会每年都支持一些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， 提供了十个讲座的重要当前研究的主题， 数学科学中一个非常重要的领域 的 讲师随后根据以下内容编写了一本简要的专著 这些演讲通常由美国人出版， 数学学会或工业与应用数学学会 数学，或由美国统计协会联合 和数理统计研究所。 某些特征 将这些会议与典型的研究区分开来 两会 （1）注重一个重要的、 由一位领先的从业者进行及时的研究领域，（2）续 （3）小组讨论 审查质量、广度和及时性，以及（4）出版 为更广泛的观众提供专题论文。

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.