Sobolev boundedness and continuity for commutators of the local Hardy–Littlewood maximal function

Författare

  • Feng Liu Shandong University of Science and Technology, College of Mathematics and System Science
  • Qingying Xue Beijing Normal University, School of Mathematical Sciences
  • Kôzô Yabuta Kwansei Gakuin University, Research Center for Mathematics and Data Science

Nyckelord:

Commutator, maximal commutator, local Hardy-Littlewood maximal function, Sobolev space, boundedness, continuity

Abstract

Let Ω be a subdomain in Rn and MΩ be the local Hardy-Littlewood maximal function. In this paper, we show that both the commutator and the maximal commutator of MΩ are bounded and continuous from the first order Sobolev spaces W1,p1(Ω) to W1,p(Ω) provided that bW1,p2(Ω), 1<p1,p2,p< and 1/p=1/p1+1/p2. These are done by establishing several new pointwise estimates for the weak derivatives of the above commutators. As applications, the bounds of these operators on the Sobolev space with zero boundary values are obtained.
Sektion
Articles

Publicerad

2021-12-31

Referera så här

Liu, F., Xue, Q., & Yabuta, K. (2021). Sobolev boundedness and continuity for commutators of the local Hardy–Littlewood maximal function. Annales Fennici Mathematici, 47(1), 203–235. https://doi.org/10.54330/afm.113296