• Title/Summary/Keyword: sublinear operator

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SOME MULTI-SUBLINEAR OPERATORS ON GENERALIZED MORREY SPACES WITH NON-DOUBLING MEASURES

  • Shi, Yanlong;Tao, Xiangxing
    • Journal of the Korean Mathematical Society
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    • v.49 no.5
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    • pp.907-925
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    • 2012
  • In this paper the boundedness for a large class of multi-sublinear operators is established on product generalized Morrey spaces with non-doubling measures. As special cases, the corresponding results for multilinear Calder$\acute{o}$n-Zygmund operators, multilinear fractional integrals and multi-sublinear maximal operators will be obtained.

SOME REMARKS ON VECTOR-VALUED TREE MARTINGALES

  • He, Tong-Jun
    • Journal of the Korean Mathematical Society
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    • v.49 no.2
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    • pp.395-404
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    • 2012
  • Our first aim of this paper is to define maximal operators a-quadratic variation and of a-conditional quadratic variation for vectorvalued tree martingales and to show that these maximal operators and maximal operators of vector-valued tree martingale transforms are all sublinear operators. The second purpose is to prove that maximal operator inequalities of a-quadratic variation and of a-conditional quadratic variation for vector-valued tree martingales hold provided 2 ${\leq}$ a < $\infty$ by means of Marcinkiewicz interpolation theorem. Based on a result of reference [10] and using Marcinkiewicz interpolation theorem, we also propose a simple proof of maximal operator inequalities for vector-valued tree martingale transforms, under which the vector-valued space is a UMD space.

Anisotropic Variable Herz Spaces and Applications

  • Aissa Djeriou;Rabah Heraiz
    • Kyungpook Mathematical Journal
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    • v.64 no.2
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    • pp.245-260
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    • 2024
  • In this study, we establish some new characterizations for a class of anisotropic Herz spaces in which all exponents are considered as variables. We also provide a description of these spaces based on bloc decomposition. As an application, we investigate the boundedness of certain sublinear operators within these function spaces.