• Title/Summary/Keyword: Multilinear operator

Search Result 19, Processing Time 0.019 seconds

WEAK FACTORIZATIONS OF H1 (ℝn) IN TERMS OF MULTILINEAR FRACTIONAL INTEGRAL OPERATOR ON VARIABLE LEBESGUE SPACES

  • Zongguang Liu;Huan Zhao
    • Bulletin of the Korean Mathematical Society
    • /
    • v.60 no.6
    • /
    • pp.1439-1451
    • /
    • 2023
  • This paper provides a constructive proof of the weak factorizations of the classical Hardy space H1(ℝn) in terms of multilinear fractional integral operator on the variable Lebesgue spaces, which the result is new even in the linear case. As a direct application, we obtain a new proof of the characterization of BMO(ℝn) via the boundedness of commutators of the multilinear fractional integral operator on the variable Lebesgue spaces.

A NOTE ON VARIATION CONTINUITY FOR MULTILINEAR MAXIMAL OPERATORS

  • Xiao Zhang
    • Bulletin of the Korean Mathematical Society
    • /
    • v.61 no.1
    • /
    • pp.207-216
    • /
    • 2024
  • This note is devoted to establishing the variation continuity of the one-dimensional discrete uncentered multilinear maximal operator. The above result is based on some refine variation estimates of the above maximal functions on monotone intervals. The main result essentially improves some known ones.