Weighted boundedness of parametric Marcinkiewicz integral and higher order commutator

2009 ◽  
Vol 25 (1) ◽  
pp. 25-39 ◽  
Author(s):  
Xinfeng Shi ◽  
Yinsheng Jiang
Keyword(s):  
Higher Order ◽  
Marcinkiewicz Integral ◽  
Parametric Marcinkiewicz Integral

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 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 problem on rough parametric Marcinkiewicz functions

2002 ◽  
Vol 72 (1) ◽  
pp. 13-22 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu ◽  
Kôzô Yabuta
Keyword(s):  
Kernel Function ◽  
Radial Function ◽  
Marcinkiewicz Integral ◽  
Area Function ◽  
Lusin Area Function ◽  
Parametric Marcinkiewicz Integral

AbstractIn this note the authors give the L2(n) boundedness of a class of parametric Marcinkiewicz integral with kernel function Ω in L log+L(Sn−1) and radial function h(|x|) ∈ l ∞ l(Lq)(+) for 1 < q ≦.As its corollary, the Lp (n)(2 < p < ∞) boundedness of and and with Ω in L log+L (Sn-1) and h(|x|) ∈ l∞ (Lq)(+) are also obtained. Here and are parametric Marcinkiewicz functions corresponding to the Littlewood-Paley g*λ-function and the Lusin area function S, respectively.

scholarly journals Riesz potential, Marcinkiewicz integral and their commutators on mixed Morrey spaces

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 931-944
Author(s):  
Andrea Scapellato
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Riesz Potential ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Higher Order ◽  
Lipschitz Class ◽  
Fractional Integral Operator ◽  
Marcinkiewicz Integral ◽  
Type Integral

This paper deals with the boundedness of integral operators and their commutators in the framework of mixed Morrey spaces. Precisely, we study the mixed boundedness of the commutator [b,I?], where I? denotes the fractional integral operator of order ? and b belongs to a suitable homogeneous Lipschitz class. Some results related to the higher order commutator [b,I?]k are also shown. Furthermore, we examine some boundedness properties of the Marcinkiewicz-type integral ?? and the commutator [b,??] when b belongs to the BMO class.

BOUNDS FOR NONISOTROPIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES

2015 ◽  
Vol 99 (3) ◽  
pp. 380-398 ◽  
Author(s):  
FENG LIU ◽  
SUZHEN MAO
Keyword(s):  
Radial Function ◽  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Marcinkiewicz Integrals ◽  
Parametric Marcinkiewicz Integral ◽  
Marcinkiewicz Operators ◽  
L Log L

In an extrapolation argument, we prove certain $L^{p}\,(1<p<\infty )$ estimates for nonisotropic Marcinkiewicz operators associated to surfaces under the integral kernels given by the elliptic sphere functions ${\rm\Omega}\in L(\log ^{+}L)^{{\it\alpha}}({\rm\Sigma})$ and the radial function $h\in {\mathcal{N}}_{{\it\beta}}(\mathbb{R}^{+})$. As applications, the corresponding results for parametric Marcinkiewicz integral operators related to area integrals and Littlewood–Paley $g_{{\it\lambda}}^{\ast }$-functions are given.

scholarly journals Generalized Parabolic Marcinkiewicz Integral Operators Related to Surfaces of Revolution

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1200
Author(s):  
Amer Darweesh ◽  
Mohammed Ali
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Surfaces Of Revolution ◽  
Parametric Marcinkiewicz Integral

In this work, the generalized parametric Marcinkiewicz integral operators with mixed homogeneity related to surfaces of revolution are studied. Under some weak conditions on the kernels, the boundedness of such operators from Triebel–Lizorkin spaces to L p spaces are established. Our results, with the help of an extrapolation argument, improve and extend some previous known results.

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