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- W4287636070 abstract "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." @default.
- W4287636070 created "2022-07-25" @default.
- W4287636070 creator A5065275841 @default.
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- W4287636070 date "2020-10-20" @default.
- W4287636070 modified "2023-09-24" @default.
- W4287636070 title "On derivatives, Riesz transforms and Sobolev spaces for Fourier-Bessel expansions" @default.
- W4287636070 doi "https://doi.org/10.48550/arxiv.2010.10376" @default.
- W4287636070 hasPublicationYear "2020" @default.
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