scholarly journals A sparse domination for the Marcinkiewicz integral with rough kernel and applications

2020 ◽  
Vol 96 (3-4) ◽  
pp. 377-399
Author(s):  
Xiangxing Tao ◽  
Guoen Hu
Keyword(s):  
Rough Kernel ◽  
Marcinkiewicz Integral

scholarly journals Existence and Boundedness of Parametrized Marcinkiewicz Integral with Rough Kernel on Campanato Spaces

2006 ◽  
Vol 181 ◽  
pp. 103-148 ◽  
Author(s):  
Yong Ding ◽  
Qingying Xue ◽  
Kôzô Yabuta
Keyword(s):  
Single Point ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Marcinkiewicz Integral ◽  
Type Condition ◽  
Lipschitz Spaces ◽  
Area Function ◽  
Bmo Function ◽  
Lusin Area Function ◽  
Lipschitz Kernel

AbstractLet g(f), S(f), g*λ(f) be the Littlewood-Paley g function, Lusin area function, and Littlewood-Paley g*λ(f) function of f, respectively. In 1990 Chen Jiecheng and Wang Silei showed that if, for a BMO function f, one of the above functions is finite for a single point in ℝn, then it is finite a.e. on ℝn, and BMO boundedness holds. Recently, Sun Yongzhong extended this result to the case of Campanato spaces (i.e. Morrey spaces, BMO, and Lipschitz spaces). One of us improved his g*λ(f) result further, and treated parametrized Marcinkiewicz functions with Lipschitz kernel μρ(f), μρs(f) and μλ*,ρ(f). In this paper, we show that the same results hold also in the case of rough kernel satisfying Lp-Dini type condition.

Boundedness of Marcinkiewicz integral with rough kernel on Triebel-Lizorkin spaces

2015 ◽  
Vol 16 (8) ◽  
pp. 654-657
Author(s):  
Chun-jie Zhang ◽  
Fang-fang Ren ◽  
Yu-huai Zhang ◽  
Gui-lian Gao
Keyword(s):  
Rough Kernel ◽  
Marcinkiewicz Integral

A note concerning Marcinkiewicz integral with rough kernel

2021 ◽  
Vol 24 (01) ◽  
pp. 2150005
Author(s):  
Feri̇t Gürbüz
Keyword(s):  
Singular Integrals ◽  
Rough Kernel ◽  
Marcinkiewicz Integral ◽  
Marcinkiewicz Integrals ◽  
Norm Inequalities

In this paper, applying some properties of rough kernel and using some technical lemmas, we prove various norm inequalities concerning Marcinkiewicz integral with rough kernel. Indeed, we extend some known results on singular integrals to Marcinkiewicz integrals.

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.

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Type Integral ◽  
Type Spaces ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

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 Boundedness of the Marcinkiewicz integrals with rough kernel associated to surfaces

2010 ◽  
Vol 62 (2) ◽  
pp. 233-262 ◽  
Author(s):  
Yong Ding ◽  
Qingying Xue ◽  
Kôzô Yabuta
Keyword(s):  
Rough Kernel ◽  
Marcinkiewicz Integrals

Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel

1998 ◽  
Vol 50 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Rough Kernel ◽  
Degree Zero ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
Image Position

AbstractGiven function Ω on ℝn , we define the fractional maximal operator and the fractional integral operator by and respectively, where 0 < α < n. In this paper we study the weighted norm inequalities of MΩα and TΩα for appropriate α, s and A(p, q) weights in the case that Ω∈ Ls(Sn-1)(s> 1), homogeneous of degree zero.

Sign in / Sign up

Export Citation Format

Share Document