Weighted Young Inequalities for Convolutions
Weighted Young Inequalities for Convolutions
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卷积的加权年轻不等式
DOI：
10.1007/s100120200030
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发表时间：
2003
影响因子：
0.2
通讯作者：
Y. Rakotondratsimba
中科院分区：
文献类型：
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作者：
Y. Rakotondratsimba
像往常一样，卷积产品，两个可测量的功能。两个人。是不是，是不是？f ≠ x ≠ y AR n g ≠ x ≠ y ≠ f ≠ y，本文中假定1 < p，q< y，p0 <$p <$1，q 0 <$q <$1，u ≠ 0。好吧，好吧。好的，谢谢。是权函数，即非负和局部可积函数。我们的目的是得到关于权的充分条件。又是一个。有一个常数C> 0，使得λ x AR n λ g？f qxxdx1/q a Ckg。kX 1、所有的f好吧，好吧。用gl使B 0。一个径向单调函数。
As usual the convolution product, of two measurable functions f ð. Þ and gð. Þ, is given by ðg? f ÞðxÞ ¼ ð y AR n gðx À yÞf ðyÞ dy, and throughout this paper it is assumed that1< p, q< y, p0 ¼ p p À 1, q0 ¼ q q À 1 and uð. Þ, vð. Þ, v1Àp0 ð. Þ, are weight functions, ie nonnegative and locally integrable functions. Our purpose is to derive sufficient conditions on the weights uð. Þ and vð. Þ for which there is a constant C> 0 such that ð x AR n ðg? f ÞqðxÞuðxÞ dx1/q a Ckgð. ÞkX ð x AR n f pðxÞvðxÞ dx1/p ð1. 1Þ for all f ð. Þ, gð. Þ b 0 with gð. Þ a radial and monotone function.