Weighted Littlewood-Paley Theory and Exponential-Square Integrability
Weighted Littlewood-Paley Theory and Exponential-Square Integrability
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DOI：
10.1007/978-3-540-74587-7
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发表时间：
2007-12
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影响因子：
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通讯作者：
Michael Wilson
中科院分区：
文献类型：
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作者：
Michael Wilson
Littlewood-Paley 理论是傅里叶分析的重要工具，具有与偏微分方程、信号处理和概率的应用和联系。它将正交性的一些好处扩展到了正交性实际上没有意义的情况。它通过让我们用非负函数的无穷级数来控制某些振荡无穷级数函数来实现这一点。从 20 世纪 80 年代开始，人们发现这种控制可以比之前想象的更加敏锐。本书试图对这些发现、它们背后的方法、它们的后果以及它们的一些应用进行温和、积极的介绍。
Littlewood-Paley theory is an essential tool of Fourier analysis, with applications and connections to PDEs, signal processing, and probability. It extends some of the benefits of orthogonality to situations where orthogonality doesn’t really make sense. It does so by letting us control certain oscillatory infinite series of functions in terms of infinite series of non-negative functions. Beginning in the 1980s, it was discovered that this control could be made much sharper than was previously suspected. The present book tries to give a gentle, well-motivated introduction to those discoveries, the methods behind them, their consequences, and some of their applications.