Parametric Marcinkiewicz integrals with rough kernels acting on weak Musielak–Orlicz Hardy spaces

2019 ◽  
Vol 13 (1) ◽  
pp. 47-63
Author(s):  
Bo Li
Keyword(s):  
Hardy Spaces ◽  
Rough Kernels ◽  
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.

scholarly journals A Note on Marcinkiewicz Integrals along Submanifolds of Finite Type

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Daiqing Zhang
Keyword(s):  
Finite Type ◽  
Unit Sphere ◽  
Radial Direction ◽  
Rough Kernels ◽  
Marcinkiewicz Integrals ◽  
Submanifolds Of Finite Type

We study the parametric Marcinkiewicz integrals along submanifolds of finite type with rough kernels. The kernels of our operators are allowed to be very rough both on the unit sphere and in the radial direction. Under the rather weakened size conditions on the integral kernels, the Lp bounds will be established for such operators. As applications, the corresponding results for parametric Marcinkiewicz integrals related to area integrals and Littlewood-Paley gλ⁎ functions are also given.

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.

BOUNDEDNESS OF SEVERAL INTEGRAL OPERATORS WITH BOUNDED VARIABLE KERNELS ON HARDY AND WEAK HARDY SPACES

2013 ◽  
Vol 24 (12) ◽  
pp. 1350095 ◽  
Author(s):  
HUA WANG
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Variable Kernel ◽  
Marcinkiewicz Integrals ◽  
Decomposition Theory ◽  
Logarithmic Type ◽  
Lipschitz Conditions

In this paper, by using the atomic decomposition theory of Hardy space H1(ℝn) and weak Hardy space WH1(ℝn), we give the boundedness properties of some operators with variable kernels such as singular integral operators, fractional integrals and parametric Marcinkiewicz integrals on these spaces, under certain logarithmic type Lipschitz conditions assumed on the variable kernel Ω(x, z).

Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels

2015 ◽  
Vol 27 (4) ◽  
Author(s):  
Yanping Chen ◽  
Yong Ding
Keyword(s):  
Rough Kernels ◽  
Marcinkiewicz Integrals

AbstractThis paper is devoted to the study of the

Sublinear operators on weighted Hardy spaces with variable exponents

2019 ◽  
Vol 31 (3) ◽  
pp. 607-617 ◽  
Author(s):  
Kwok-Pun Ho
Keyword(s):  
Hardy Spaces ◽  
Variable Exponents ◽  
Square Functions ◽  
Weighted Hardy Spaces ◽  
Riesz Means ◽  
Marcinkiewicz Integrals ◽  
Sublinear Operators ◽  
Intrinsic Square Functions

Abstract We establish the mapping properties for some sublinear operators on weighted Hardy spaces with variable exponents by using extrapolation. In particular, we study the Calderón–Zygmund operators, the maximal Bochner–Riesz means, the intrinsic square functions and the Marcinkiewicz integrals on weighted Hardy spaces with variable exponents.

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