Results 21 to 30 of about 2,945 (178)

On Marcinkiewicz Integral with Homogeneous Kernels

Journal of Mathematical Analysis and Applications, 2000
The authors improve the boundedness theorems of the Marcinkiewicz integral \(\mu_\Omega\) on \(\roman{BMO}(\mathbb R^n)\) and the Campanato spaces \(\mathcal E^{\alpha, p}(\mathbb R^n)\). Recall the Campanato spaces. A locally integrable function \(f(x)\) is said to belong to \(\mathcal E^{\alpha, p}(\mathbb R^n)\) if \(\|f\|_{\alpha,p}=\sup_Q |Q ...
Ding, Yong, Lu, Shanzhen, Xue, Qingying
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On the commutator of the Marcinkiewicz integral

Journal of Mathematical Analysis and Applications, 2003
Let \(n\geq 2\) and \(S^{n-1}\) be the unit sphere in \(\mathbb{R}^n\) equipped with the normalized Lebesgue measure \(d\sigma\). Suppose that \(\Omega\) is a homogeneous function of degree zero on \(\mathbb{R}^n\) that satisfies \(\Omega\in L(S^{n-1})\) and \(\int_{S^{n-1}}\Omega\,d\sigma= 0\).
Hu, Guoen, Yan, Dunyan
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On Rough Parametric Marcinkiewicz Integrals Along Certain Surfaces

Mathematics
In this paper, we study rough Marcinkiewicz integrals associated with surfaces defined by ΨP,ϕ={(˜P(w),ϕ(w)):w∈Rm}. We establish the Lp-boundedness of these integrals when the kernel functions lie in the Lq(Sm−1) space.
Mohammed Ali, Hussain Al-Qassem
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SOME REMARKS ON MARCINKIEWICZ INTEGRALS ALONG SUBMANIFOLDS [PDF]

Taiwanese Journal of Mathematics, 2012
We investigate the $L^p$ boundedness for a class of parametric Marcinkiewicz integral operators associated to submanifolds under the $L(\log L)^{\alpha}({S}^{n-1})$ or Block space condition on the kernel functions. Our results improve the recent results by Al-Qassem and Pan in Studia Mathematica.
Wenjuan Li, Kôzô Yabuta
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Rough Marcinkiewicz integral operators [PDF]

International Journal of Mathematics and Mathematical Sciences, 2001
We study the Marcinkiewicz integral operator , where 𝒫 is a polynomial mapping from ℝn into ℝd and Ω is a homogeneous function of degree zero on ℝn with mean value zero over the unit sphere Sn−1. We prove an Lp boundedness result of M𝒫 for rough Ω.
Hussain Al-Qassem, Ahmad Al-Salman
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On certain estimates for Marcinkiewicz integrals and extrapolation

Collectanea mathematica, 2009
Let \(\mathbb R^n\), \(n\geq2\), be the \(n\)-dimensional Euclidean space and \(S^{n-1}\) be the unit sphere in \(\mathbb R^n\) with area element \(d\sigma(x')\) on \(S^{n-1}\). Let \(\Omega(x)|x|^{-n}\) be a homogeneous function of degree \(-n\) on \(\mathbb R^n\), with \(\Omega\in L^1(S^{n-1})\) and \(\int_{S^{n-1}}\Omega(x')\,d\sigma(x')=0\), where \
Al-Qassem, Hussain, Pan, Yibiao
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On Certain Estimates for Parabolic Marcinkiewicz Integrals Related to Surfaces of Revolution on Product Spaces and Extrapolation

Axioms, 2022
In this paper, appropriate Lp bounds for particular classes of parabolic Marcinkiewicz integrals along surfaces of revolution on product spaces are obtained.
Mohammed Ali, Hussain Al-Qassem
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The existence and boundedness of linear and multilinear Marcinkiewicz integrals on central Campanato spaces

Journal of Inequalities and Applications, 2020
In this paper, we obtain the existence and boundedness of Marcinkiewicz integrals with homogeneous kernels on central Campanato spaces. Moreover, the existence and boundedness of multilinear Marcinkiewicz integrals on central Campanato spaces are also ...
Jiao Ma, Mingquan Wei, Dunyan Yan
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Rough Marcinkiewicz integral operators on product spaces

Collectanea Mathematica, 2005
Let \(d\geq 2\) (\(d= n\) or \(d=m\)) and \(S^{d-1}\) be the unit sphere in \(\mathbb{R}^d\) equipped with the normalized Lebesgue measure \(d\sigma\). Suppose that \(\Omega(x,y)\) is a homogeneous function of degree zero in both variables \(x\) and \(y\) and it satisfies \(\Omega\in L(S^{n-1}\times S^{m-1})\) and \[ \int_{S^{n-1}} \Omega(x,y)\,d\sigma(
Hussain Al-Qassem
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$L^{p}$ BOUNDS FOR MARCINKIEWICZ INTEGRALS [PDF]

Proceedings of the Edinburgh Mathematical Society, 2003
AbstractIn this paper the authors establish the $L^p$ boundedness for several classes of Marcinkiewicz integral operators with kernels satisfying a condition introduced by Grafakos and Stefanov in Indiana Univ. Math.
Ding, Yong, Pan, Yibiao
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