On the Generalized Marcinkiewicz Integral Operators with Rough Kernels

2011 ◽  
Vol 54 (1) ◽  
pp. 100-112 ◽  
Author(s):  
Dashan Fan ◽  
Huoxiong Wu
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Rough Kernels

AbstractA class of generalized Marcinkiewicz integral operators is introduced, and, under rather weak conditions on the integral kernels, the boundedness of such operators on Lp and Triebel–Lizorkin spaces is established.

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 Marcinkiewicz integrals along subvarieties on product domains

2004 ◽  
Vol 2004 (72) ◽  
pp. 4001-4011
Author(s):  
Ahmad Al-Salman
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Rough Kernels ◽  
Marcinkiewicz Integrals ◽  
Product Domains

We study theLpmapping properties of a class of Marcinkiewicz integral operators on product domains with rough kernels supported by subvarieties.

scholarly journals A note on maximal singular integrals with rough kernels

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiao Zhang ◽  
Feng Liu
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Maximal Operators ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Homogeneous Mapping ◽  
Recent Developments ◽  
Maximal Singular Integrals ◽  
Maximal Singular Integral

Abstract In this note we study the maximal singular integral operators associated with a homogeneous mapping with rough kernels as well as the corresponding maximal operators. The boundedness and continuity on the Lebesgue spaces, Triebel–Lizorkin spaces, and Besov spaces are established for the above operators with rough kernels in $H^{1}({\mathrm{S}}^{n-1})$ H 1 ( S n − 1 ) , which complement some recent developments related to rough maximal singular integrals.

On a Class of Singular Integral Operators With Rough Kernels

2006 ◽  
Vol 49 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Ahmad Al-Salman
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Functions ◽  
Rough Kernels ◽  
Block Spaces ◽  
Size Condition

AbstractIn this paper, we study the Lp mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces. We prove that our operators are bounded on Lp provided that their kernels satisfy a size condition much weaker than that for the classical Calderón–Zygmund singular integral operators. Moreover, we present an example showing that our size condition is optimal. As a consequence of our results, we substantially improve a previously known result on certain maximal functions.

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.

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

Marcinkiewicz integral operators on product domains

2002 ◽  
Vol 132 (3) ◽  
pp. 523-530
Author(s):  
KYUNG SOO RIM
Keyword(s):  
Integral Operator ◽  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Cancellation Property ◽  
Product Domains ◽  
Marcinkiewicz Integral Operator

With the cancellation property of the bounded kernel, we prove that the generalized Marcinkiewicz integral operator is bounded on L2 (ℝn×ℝm) for all dimensions n, m.

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