Abstract
We prove a Hardy inequality for ultraspherical expansions by using a proper ground state representation. From this result we deduce some uncertainty principles for this kind of expansions. Our result also implies a Hardy inequality on spheres with a potential having a double singularity.
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Acknowledgements
Research of Óscar Ciaurri supported by Grant No. MTM2015-65888-C4-4-P of the Spanish Government.
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Communicated by Krzysztof Stempak.
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Arenas, A., Ciaurri, Ó. & Labarga, E. A Hardy Inequality for Ultraspherical Expansions with an Application to the Sphere. J Fourier Anal Appl 24, 416–430 (2018). https://doi.org/10.1007/s00041-017-9531-0
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DOI: https://doi.org/10.1007/s00041-017-9531-0