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Funktsional'nyi Analiz i ego Prilozheniya, 2021, Volume 55, Issue 4, Pages 63–77
DOI: https://doi.org/10.4213/faa3815
(Mi faa3815)
 

This article is cited in 1 scientific paper (total in 1 paper)

Dunkl Translations, Dunkl-Type BMO Space, and Riesz Transforms for the Dunkl Transform on $L^\infty$

W. Teng

School of Science and Technology, Kwansei Gakuin University
Full-text PDF (660 kB) Citations (1)
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Abstract: In this paper we will give some results on the support of Dunkl translations on compactly supported functions. Then we will define the Dunkl-type BMO space and Riesz transforms for the Dunkl transform on $L^\infty$ and prove the boundedness of the Riesz transforms from $L^\infty$ to the Dunkl-type BMO space under the assumption of the uniform boundedness of Dunkl translations. The proof and the definition in the Dunkl setting will be harder than in the classical case for the lack of some properties of Dunkl translations similar to those of classical translations. We will also extend Gallardo and Rejeb's precise description of the support of Dunkl translations on characteristic functions to all nonnegative radial functions in $L^2(m_k)$.
Keywords: Dunkl translations, Riesz transforms, Dunkl-type BMO space.
Received: 02.07.2020
Revised: 05.07.2021
Accepted: 12.07.2021
English version:
Functional Analysis and Its Applications, 2021, Volume 55, Issue 4, Pages 304–315
DOI: https://doi.org/10.1134/S0016266321040055
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: W. Teng, “Dunkl Translations, Dunkl-Type BMO Space, and Riesz Transforms for the Dunkl Transform on $L^\infty$”, Funktsional. Anal. i Prilozhen., 55:4 (2021), 63–77; Funct. Anal. Appl., 55:4 (2021), 304–315
Citation in format AMSBIB
\Bibitem{Ten21}
\by W.~Teng
\paper Dunkl Translations, Dunkl-Type BMO Space, and Riesz Transforms for the Dunkl Transform on $L^\infty$
\jour Funktsional. Anal. i Prilozhen.
\yr 2021
\vol 55
\issue 4
\pages 63--77
\mathnet{http://mi.mathnet.ru/faa3815}
\crossref{https://doi.org/10.4213/faa3815}
\transl
\jour Funct. Anal. Appl.
\yr 2021
\vol 55
\issue 4
\pages 304--315
\crossref{https://doi.org/10.1134/S0016266321040055}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000770340500005}
Linking options:
  • https://www.mathnet.ru/eng/faa3815
  • https://doi.org/10.4213/faa3815
  • https://www.mathnet.ru/eng/faa/v55/i4/p63
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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    Full-text PDF :59
    References:43
    First page:19
     
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