Harmonic Analysis in China is a collection of surveys and research papers written by distinguished Chinese mathematicians from within the People's Republic of China and expatriates. The book covers topics in analytic function spaces of several complex variables, integral transforms, harmonic analysis on classical Lie groups and manifolds, LP- estimates of the Cauchy-Riemann equations and wavelet transforms. The reader will also be able to trace the great influence of the late Professor Loo-keng Hua's ideas and methods on research into harmonic analysis on classical domains and the theory of functions of several complex variables. Western scientists will thus become acquainted with the unique features and future trends of harmonic analysis in China. Audience: Analysts, as well as engineers and physicists who use harmonic analysis.
Table of ContentsPreface. Contributors. On LP Estimates of the Cauchy-Riemann Equations; D.-C. Chang, C. Fefferman. Recent Progress in Hardy Spaces on Manifolds; J.-C. Chen, S.-Lei Wang. Calderon-Zygmund Operator Theory and Function Spaces; D.-Gao, Y.-S. Han. Hp Theory on Compact Lie Groups; D.-S. Fan. The Unitary Dual Covering Groups of GL(n) Over a Local Field; J.-S. Huang. Casimir Operator and Wavelet Transform; Q.-T. Jiang, L.-Z. Peng. Oscillatory Singular Integrals with Rough Kernel; Y.-S. Jiang, S.- Z. Lu. The Minimal Decay of Matrix Coefficients for Classical Groups; J.-S. Li. Applications of Harmonic Analysis in Geophysics; S.-X. Li. Bivariate Box-Spine Wavelets; X.-Z. Liang et al. On Martingale Spaces and Inequalities; R.-L. Long. Uniform Weak (1,1) Bounds for Oscillatory Singular Integrals; Y.-B. Pan. Paracommutators and Hankel Operators; L.-Z. Peng. Operators-Derivatives-Spaces- Differential Equations on Locally Compact Vilenkin Groups; W.-Y. Su. On Selfsimilarity of Functions; W.-X. Zheng. Harmonic Analysis on Compact Lie Groups and Compact Homogeneous Spaces in China; X.-A. Zheng. Harmonic Analysis on Bounded Symmetric Domains; K.-H. Zhu.