Please wait a minute...
高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2014, Vol. 29 Issue (3): 361-368    DOI:
    
Boundedness of commtuators of parametric Marcinkiewicz integrals on Hardy spaces with non-doubling measures
ZHOU Jiang, LU Guang-hu
College of Mathematics and System Sciences, Xinjiang Univ, Urumqi 830046, China
Download:   PDF(0KB)
Export: BibTeX | EndNote (RIS)      

Abstract  In this paper, the authors prove the boundedness of the commutator $\mathcal{M}^{\rho}_{b}$ generated by the parameter Marcinkiewicz integral $\mathcal{M}^{\rho}$ with Lipschitz function $b$. Under the assumption that the kernel of $\mathcal{M}$ satisfies certain condition, the authors prove that $\mathcal{M}^{\rho}_{b}$ is bounded from the Lebesgue space $L^{\frac{n}{n-\beta}}(\mu)$ to the Hardy space $H^{1}(\mu)$, and from the Lebesgue space $L^{\frac{n}{\beta}}(\mu)$ to the space $\mathrm{RBMO}(\mu)$.

Key words： non-doubling measure      parametric Marcinkiewicz integral      ${\rm Lip_{\beta}}(\mu)$      Hardy space     
Received: 29 July 2013      Published: 10 June 2018
CLC:  O174.2  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
ZHOU Jiang
LU Guang-hu
Cite this article:

ZHOU Jiang, LU Guang-hu. Boundedness of commtuators of parametric Marcinkiewicz integrals on Hardy spaces with non-doubling measures. Applied Mathematics A Journal of Chinese Universities, 2014, 29(3): 361-368.

URL:

http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2014/V29/I3/361


具有非倍测度的参数型Marcinkiewicz积分交换子在Hardy空间的有界性

主要证明了由参数型Marcinkiewicz积分$\mathcal{M}^{\rho}$和Lipschitz函数$b$生成的交换子$\mathcal{M}_{b}^{\rho}$的有界性. 在$\mathcal{M}$的核满足一定的条件下, 证明了$\mathcal{M}^{\rho}_{b}$不仅从Lebesgue空间$L^{\frac{n}{n-\beta}}(\mu)$ 到Hardy空间$H^{1}(\mu)$有界, 而且从Lebesgue空间$L^{n/\beta}(\mu)$ 到$\mathrm{RBMO}(\mu)$有界.

关键词： 非倍测度,  参数型Marcinkiewicz积分,  ${\rm Lip_\beta}(\mu)$函数,  Hardy空间 
[1] HUANG Qiang, WANG Zheng. Some applications on rearrangement[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(2): 217-228.