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TWO-WEIGHTED CONDITIONS AND CHARACTERIZATIONS FOR A CLASS OF MULTILINEAR FRACTIONAL NEW MAXIMAL OPERATORS

  • Rui Li (College of Mathematics and Statistics Northwest Normal University) ;
  • Shuangping Tao (College of Mathematics and Statistics Northwest Normal University)
  • Received : 2022.05.22
  • Accepted : 2022.09.26
  • Published : 2023.01.01

Abstract

In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator 𝓜ϕ,β are established. Meanwhile, we introduce the ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ conditions and obtain the characterization of two-weighted inequalities for 𝓜ϕ,β. Finally, the relationships of the conditions ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi}),\,{\mathcal{A}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ and the characterization of the one-weight $A_{({\vec{p}},q),{\beta}}({\varphi})$ are given.

Keywords

Acknowledgement

This work was financially supported by the National Natural Science Foundation of China(Grant No. 11561062).

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