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Riesz Transforms And Multipliers For The Bessel-Grushin Operator
Univ La Laguna, Dept Anal Matemat, Campus Anchieta, San Cristobal la Laguna 38271, Sta Cruz De Ten, Spain..
Univ La Laguna, Dept Anal Matemat, Campus Anchieta, San Cristobal la Laguna 38271, Sta Cruz De Ten, Spain..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Univ Las Palmas Gran Canaria, Dept Matemat, Campus Tafira Baja, Las Palmas Gran Canaria 35017, Spain..
2016 (English)In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 128, 51-106 p.Article in journal (Refereed) PublishedText
Abstract [en]

We establish that the spectral multiplier m(G(alpha)) associated to the differential operator G alpha = -Delta x + Sigma j=1m alpha j2-1/4/xj2 - vertical bar x vertical bar 2 Delta(y) on (0, infinity)(m) x R-n, which we call the Bessel-Grushin operator, is of weak type (1, 1) provided that m is in a suitable local Sobolev space. In order to do this, we prove a suitable weighted Plancherel estimate. Also, we study L-p-boundedness properties of Riesz transforms associated to G(alpha) in the case n = 1.

Place, publisher, year, edition, pages
2016. Vol. 128, 51-106 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-296782DOI: 10.1007/s11854-016-0002-3ISI: 000373403500002OAI: oai:DiVA.org:uu-296782DiVA: diva2:939980
Available from: 2016-06-20 Created: 2016-06-20 Last updated: 2016-06-20Bibliographically approved

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Castro, Alejandro J.
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