论文标题
关于衍生物，Riesz转换和Sobolev空间用于傅立叶贝塞尔的扩展
On derivatives, Riesz transforms and Sobolev spaces for Fourier-Bessel expansions
论文作者
论文摘要
我们研究了与离散傅里叶贝塞尔扩展相关的适当选择的衍生物问题。我们介绍了一种新的所谓基本测量傅里贝斯设置，其中相关的衍生物仅仅是普通的导数。然后，我们在这种情况下研究Riesz变换和Sobolev空间。我们的主要结果是Riesz变换的$ L^P $结合度（即使在多维情况下）以及Sobolev和傅立叶贝塞尔潜在空间之间的同构。此外，在本文中，我们收集了有关文献早期考虑的另外两个紧密相关的傅里叶贝塞尔情况的各种评论。我们认为，我们的观察结果对傅立叶贝塞尔扩张的分析有了一些新的启示。
We study the problem of an appropriate choice of derivatives associated with discrete Fourier-Bessel expansions. We introduce a new so-called essential measure Fourier-Bessel setting, where the relevant derivative is simply the ordinary derivative. Then we investigate Riesz transforms and Sobolev spaces in this context. Our main results are $L^p$-boundedness of the Riesz transforms (even in a multi-dimensional situation) and an isomorphism between the Sobolev and Fourier-Bessel potential spaces. Moreover, throughout the paper we collect various comments concerning two other closely related Fourier-Bessel situations that were considered earlier in the literature. We believe that our observations shed some new light on analysis of Fourier-Bessel expansions.
