商品描述
These notes give the basic ingredients of the theory of weighted Hardy spaces of tempered distribution on Rn and illustrate the techniques used. The authors consider properties of weights in a general setting; they derive mean value inequalities for wavelet transforms and introduce halfspace techniques with, for example, nontangential maximal functions and g-functions. This leads to several equivalent definitions of the weighted Hardy space HPW. Fourier multipliers and singular integral operators are applied to the weighted Hardy spaces and complex interpolation is considered. One tool often used here is the atomic decomposition. The methods developed by the authors using the atomic decomposition in the strictly convex case p>1 are of special interest.
商品描述(中文翻譯)
這些筆記提供了有關 Rn 上的加權 Hardy 空間的溫和分佈理論的基本要素，並說明了所使用的技術。作者在一般情境下考慮了權重的性質；他們推導了小波變換的均值不等式，並引入了半空間技術，例如非切向的最大函數和 g 函數。這導致了加權 Hardy 空間 HPW 的幾個等價定義。傅立葉乘子和奇異積分算子被應用於加權 Hardy 空間，並考慮了複數插值。這裡經常使用的一個工具是原子分解。作者在嚴格凸的情況下（p>1）使用原子分解所發展的方法特別引人注目。
