The boundedness of commutators of multilinear Marcinkiewicz integral

2020 ◽  
Vol 195 ◽  
pp. 111727
Author(s):  
Sha He ◽  
Yiyu Liang
Keyword(s):  
Marcinkiewicz Integral

scholarly journals Generalized parabolic Marcinkiewicz integrals associated with polynomial compound curves with rough kernels

2020 ◽  
Vol 53 (1) ◽  
pp. 44-57
Author(s):  
Mohammed Ali ◽  
Qutaibeh Katatbeh
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Rough Kernels ◽  
Marcinkiewicz Integrals ◽  
Natural Extensions ◽  
Parametric Marcinkiewicz Integral ◽  
Weaker Conditions

AbstractIn this article, we study the generalized parabolic parametric Marcinkiewicz integral operators { {\mathcal M} }_{{\Omega },h,{\Phi },\lambda }^{(r)} related to polynomial compound curves. Under some weak conditions on the kernels, we establish appropriate estimates of these operators. By the virtue of the obtained estimates along with an extrapolation argument, we give the boundedness of the aforementioned operators from Triebel-Lizorkin spaces to Lp spaces under weaker conditions on Ω and h. Our results represent significant improvements and natural extensions of what was known previously.

Erratum: "On Marcinkiewicz integral with variable kernels", Vol. 53 (2004), 805-822

2007 ◽  
Vol 56 (2) ◽  
pp. 991-994 ◽  
Author(s):  
Chin-cheng Lin ◽  
Yong Ding ◽  
Ying-Chieh Lin
Keyword(s):  
Marcinkiewicz Integral

On Marcinkiewicz integral with variable kernels

2004 ◽  
Vol 53 (3) ◽  
pp. 805-822 ◽  
Author(s):  
Yong Ding ◽  
Chin-Cheng Lin ◽  
Shuanglin Shao
Keyword(s):  
Marcinkiewicz Integral

scholarly journals Parabolic Marcinkiewicz integrals on product spaces and extrapolation

2016 ◽  
Vol 14 (1) ◽  
pp. 649-660 ◽  
Author(s):  
Mohammed Ali ◽  
Mohammed Al-Dolat
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Product Spaces ◽  
Marcinkiewicz Integrals ◽  
Product Domains

Abstract In this paper, we study the the parabolic Marcinkiewicz integral ${\cal M}_{\Omega, h}^{{\rho _{1,}}{\rho _2}}$ on product domains Rn × Rm (n, m ≥ 2). Lp estimates of such operators are obtained under weak conditions on the kernels. These estimates allow us to use an extrapolation argument to obtain some new and improved results on parabolic Marcinkiewicz integral operators.

Marcinkiewicz integral on hardy spaces

2002 ◽  
Vol 42 (2) ◽  
pp. 174-182 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu ◽  
Quigying Xue
Keyword(s):  
Hardy Spaces ◽  
Marcinkiewicz Integral

Fractional type Marcinkiewicz integral operators on function spaces

2015 ◽  
Vol 27 (5) ◽  
Author(s):  
Qingying Xue ◽  
Kôzô Yabuta ◽  
Jingquan Yan
Keyword(s):  
Integral Operators ◽  
Function Spaces ◽  
Marcinkiewicz Integral ◽  
Fractional Type

AbstractIn this paper, we discussed about the boundedness of the fractional type Marcinkiewicz integral operators, and improved a result given by Chen, Fan and Ying in 2002. They showed that under certain conditions the fractional type Marcinkiewicz integral operators are bounded from the Triebel–Lizorkin spaces

scholarly journals Marcinkiewicz Integrals on Weighted Weak Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yue Hu ◽  
Yueshan Wang
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Lebesgue Space ◽  
Muckenhoupt Weight ◽  
Marcinkiewicz Integral ◽  
Smoothness Condition ◽  
Weight Class ◽  
Marcinkiewicz Integrals ◽  
Weak Hardy Space ◽  
Weak Lebesgue Space

We prove that, under the conditionΩ∈Lipα, Marcinkiewicz integralμΩis bounded from weighted weak Hardy spaceWHwpRnto weighted weak Lebesgue spaceWLwpRnformaxn/n+1/2,n/n+α<p≤1, wherewbelongs to the Muckenhoupt weight class. We also give weaker smoothness condition assumed on Ω to imply the boundedness ofμΩfromWHw1ℝntoWLw1Rn.

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