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Hardy spaces with variable exponents on RD-spaces and applications

Tom 520 / 2016

Ciqiang Zhuo, Yoshihiro Sawano, Dachun Yang Dissertationes Mathematicae 520 (2016), 1-74 MSC: Primary 42B30; Secondary 42B25, 42B20, 42B35, 47B06, 30L99. DOI: 10.4064/dm744-9-2015 Opublikowany online: 28 October 2016

Streszczenie

In this article, the authors introduce Hardy spaces with variable exponents, $H^{\ast,p(\cdot)}(\mathcal X)$, on RD-spaces with infinite measures via the grand maximal function. Then the authors characterize these spaces by means of the non-tangential maximal function or the dyadic maximal function. Characterizations in terms of atoms or Littlewood–Paley functions are also established. As applications, the authors prove an Olsen inequality for fractional integral operators and the boundedness of singular integral operators and quasi-Banach valued sublinear operators on these spaces. Finally, a duality theory of these spaces is developed.

Autorzy

  • Ciqiang ZhuoSchool of Mathematical Sciences
    Beijing Normal University
    Laboratory of Mathematics and Complex Systems
    Ministry of Education
    Beijing 100875, People’s Republic of China
    e-mail
  • Yoshihiro SawanoDepartment of Mathematics and Information Science
    Tokyo Metropolitan University
    1-1 Minami-Ohsawa, Hachioji, 192-0397, Tokyo, Japan
    e-mail
  • Dachun YangSchool of Mathematical Sciences
    Beijing Normal University
    Laboratory of Mathematics and Complex Systems
    Ministry of Education
    Beijing 100875, People’s Republic of China
    e-mail

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