Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions

  1. Ciaurri, O. 2
  2. Nowak, A. 3
  3. Roncal, L. 1
  1. 1 Basque Center for Applied Mathematics
    info

    Basque Center for Applied Mathematics

    Bilbao, España

    ROR 03b21sh32

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  3. 3 Institute of Mathematics, Polish Academy of Sciences, Warszawa, Poland
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Revista:
SIAM Journal on Mathematical Analysis

ISSN: 0036-1410

Any de publicació: 2017

Volum: 49

Número: 6

Pàgines: 4402-4439

Tipus: Article

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DOI: 10.1137/17M1117756 SCOPUS: 2-s2.0-85040037518 WoS: WOS:000418671600003 GOOGLE SCHOLAR

Altres publicacions en: SIAM Journal on Mathematical Analysis

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2016/00008/001

Resum

We investigate a generalized spherical means operator, in other words the generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of the corresponding kernel. As the main result, we prove two-weight mixed norm estimates for the integral operator, with general power weights involved. This leads to weighted Strichartz-Type estimates for solutions to certain Cauchy problems for classical Euler{Poisson{Darboux and wave equations with radial initial data. © 2017 Society for Industrial and Applied Mathematics.