On the boundedness of Marcinkiewicz integrals on continual variable exponent Herz spaces

2019 ◽  
Vol 26 (1) ◽  
pp. 105-116 ◽  
Author(s):  
Alexander Meskhi ◽  
Humberto Rafeiro ◽  
Muhammad Asad Zaighum
Keyword(s):  
Variable Exponent ◽  
Marcinkiewicz Integral ◽  
Herz Spaces ◽  
Marcinkiewicz Integrals

AbstractIn this paper, we obtain the boundedness of the Marcinkiewicz integral on continual Herz spaces with variable exponent, where all parameters defining the space are variable.

scholarly journals Higher-Order Commutators of Parametric Marcinkiewicz Integrals on Herz Spaces with Variable Exponent

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Hongbin Wang ◽  
Dunyan Yan
Keyword(s):  
Variable Exponent ◽  
Homogeneous Function ◽  
Higher Order ◽  
Marcinkiewicz Integral ◽  
Degree Zero ◽  
Herz Spaces ◽  
Marcinkiewicz Integrals ◽  
Bmo Functions ◽  
Parametric Marcinkiewicz Integral ◽  
Marcinkiewicz Integral Operator

LetΩ∈Ls(Sn-1)fors⩾1be a homogeneous function of degree zero andbbe BMO functions. In this paper, we obtain some boundedness of the parametric Marcinkiewicz integral operatorμΩρand its higher-order commutator[bm,μΩρ]on Herz spaces with variable exponent.

scholarly journals On the commutator of Marcinkiewicz integrals with rough kernels in variable Morrey type spaces

2020 ◽  
Vol 72 (7) ◽  
pp. 928-944
Author(s):  
M. Qu ◽  
L. Wang
Keyword(s):  
Variable Exponent ◽  
Herz Spaces ◽  
Rough Kernels ◽  
Marcinkiewicz Integrals ◽  
Type Spaces

UDC 517.5 In the framework of variable exponent Morrey and Morrey–Herz spaces, we prove some boundedness results for the commutator of Marcinkiewicz integrals with rough kernels. The approach is based on the theory of variable exponent and on generalization of the BMO-norms.

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.

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.

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.

scholarly journals Multilinear Singular Integrals and Commutators on Herz Space with Variable Exponent

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Amjad Hussain ◽  
Guilian Gao
Keyword(s):  
Singular Integral ◽  
Variable Exponent ◽  
Singular Integrals ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Herz Space ◽  
Herz Spaces ◽  
Multilinear Singular Integrals

The paper establishes some sufficient conditions for the boundedness of singular integral operators and their commutators from products of variable exponent Herz spaces to variable exponent Herz spaces.

scholarly journals Higer-order commutators of parametrized Marcinkewicz integrals on Herz spaces with variable exponent

2020 ◽  
Vol 3 (1) ◽  
pp. 56-70
Author(s):  
Omer Abdalrhman ◽  
◽  
Afif Abdalmonem ◽  
Shuangping Tao ◽  
◽  
...  
Keyword(s):  
Variable Exponent ◽  
Herz Spaces
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