论文标题
Hardy-Littlewood型定理用于$ \ r^d $中的傅立叶变换
Hardy-Littlewood-type theorems for Fourier transforms in $\R^d$
论文作者
论文摘要
我们在任何$ 1 <p <\ infty $涉及Hardy-Cesàro和Hardy-Bellman操作员的$ 1 <p <\ infty $中获得加权$ L_P $空间的傅立叶不等式。我们将这些结果扩展到$ p \ le 1 $的产品耐寒空间。此外，讨论了在各个空间（Lebesgue，Hardy，bmo）中强硬式和Hardy-Bellman运营商的界限。我们的主要工具之一是Hardy-Littlewood-Paley不等式的适当版本$ \ | \ wideHat {f} \ | _ {l_ {l_ {p'{p'，q}} \ sillesim \ silysim \ less \ left \ | f \ | f \ | _ {l_ {l_ {l_ {p，q}} $。
We obtain Fourier inequalities in the weighted $L_p$ spaces for any $1<p<\infty$ involving the Hardy-Cesàro and Hardy-Bellman operators. We extend these results to product Hardy spaces for $p\le 1$. Moreover, boundedness of the Hardy-Cesàro and Hardy-Bellman operators in various spaces (Lebesgue, Hardy, BMO) is discussed. One of our main tools is an appropriate version of the Hardy-Littlewood-Paley inequality $ \|\widehat{f}\|_{L_{p',q}} \lesssim \left\|f\right\|_{L_{p,q}}$.
