Results 161 to 170 of about 4,440 (181)

On Marcinkiewicz integral with variable kernels

Indiana University Mathematics Journal, 2004
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 \(\Omega(x,y)\) is a homogeneous function of degree zero on \(y\in\mathbb{R}^n\) and satisfies \(\Omega(x,.)\in L(S^{n-1})\) and \(\int_{S^{n-1}}\Omega(x, y')\,d\sigma(y)= 0\) for each \(x\in\mathbb{R}^n\).
Ding, Yong, Lin, Chin-Cheng, Shao, Shuanglin   +2 more
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On rough Marcinkiewicz integrals along surfaces

Acta Mathematica Sinica, English Series, 2010
Let \(\mathbb R^n\), \(n\geq2\), be the \(n\)-dimensional Euclidean space and \(S^{n-1}\) the unit sphere in \(\mathbb R^n\) equipped with the normalized Lebesgue measure \(d\sigma\). Let \(\Omega\) be a homogeneous function of degree zero on \(\mathbb R^n\) with \(\Omega\in L^1(S^{n-1})\) and \[ \int_{S^{n-1}}\Omega(y')\,d\sigma(y')=0,\tag ...
Wu,HX, Xu,JK
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Marcinkiewicz Integrals with Non-Doubling Measures

Integral Equations and Operator Theory, 2007
Let μ be a positive Radon measure on \({\mathbb{R}}^d\) which may be non doubling. The only condition that μ must satisfy is μ(B(x, r)) ≤ Crn for all \(x \in {\mathbb{R}}^d\) , r > 0 and some fixed constants C > 0 and n ∈ (0, d]. In this paper, we introduce the Marcinkiewicz integral related to a such measure with kernel satisfying some Hormander-type ...
Guoen Hu, Haibo Lin, Dachun Yang
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Marcinkiewicz integral on weighted Hardy spaces

Archiv der Mathematik, 2003
Let \(\Omega\) be a homogeneous function of degree zero on \(\mathbb R^n\) where \(n \geq 2\). We assume that \(\Omega \in L^1(S^{n-1})\) and \(\int_{S^{n-1}} \Omega(x')dx' =0\) where \(x' = x/| x |\). Then the Marcinkiewicz integral operator \(\mu_{\Omega}\) on \(\mathbb R^d\) is defined by \[ \mu_{\Omega} f(x) = \Bigl( \int_0^{\infty}| F_{\Omega, t ...
Ding, Yong, Lee, Ming-Yi, Lin, Chin-Cheng   +2 more
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On parametric marcinkiewicz integrals related to block spaces

Applied Mathematics-A Journal of Chinese Universities, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wu, Huoxiong, Zhang, Pu
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Two operators related to Marcinkiewicz integrals

Acta Mathematica Sinica, English Series, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mo, Hui Xia, Lu, Shan Zhen
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Marcinkiewicz exponents and integrals over non‐rectifiable paths

Mathematical Methods in the Applied Sciences, 2015
We introduce and study certain distributions generalizing the operation of curvilinear integration for the case where the path of integration is not rectifiable. Then we apply that distributions for solving of boundary value problems of Riemann—Hilbert type in domains with non‐rectifiable boundaries. Copyright © 2015 John Wiley & Sons, Ltd.
Kats B., Katz D.
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Lp estimates for rough parametric Marcinkiewicz integrals

SUT Journal of Mathematics, 2004
Summary: We prove the \(L^p\)-boundedness of a class of parametric Marcinkiewicz integral operators \({\mathcal M}^\rho_{\Omega, h}\) when \(h\) satisfies a certain integrability condition and \(\Omega\) belongs to the block space \(B_q^{(0,-1/2)}({\mathbf S}^{n-1})\) for some \(q>1\), \(n\geq 2\). Also, we obtain the \(L^p\)-boundedness for a class of
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Rough Marcinkiewicz integrals along certain smooth curves

Frontiers of Mathematics in China, 2012
Let \(\Omega \in L^1(S^{m-1} \times S^{n-1})\) be satisfying \(\Omega(sx,ty)=\Omega(x,y)\) for \(s,t>0\) and \[ \int_{S^{m-1}}\Omega(u',\cdot)d\sigma(u') = \int_{S^{n-1}}\Omega(\cdot, v')d\sigma(v') =0. \] For suitable functions \(\varphi, \psi: {\mathbb R}^+ \to {\mathbb R}\), the multiple Marcinkiewicz integral operator is defined by \[ {\mathcal{M ...
Ma, Bolin, Wu, Huoxiong, Zhao, Xiating
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Marcinkiewicz integral operators on product domains

Mathematical Proceedings of the Cambridge Philosophical Society, 2002
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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