Results 11 to 20 of about 2,945 (178)
Generalized parabolic Marcinkiewicz integrals associated with polynomial compound curves with rough kernels [PDF]
Demonstratio Mathematica, 2020 In this article, we study the generalized parabolic parametric Marcinkiewicz integral operators ℳΩ,h,Φ,λ(r){ {\mathcal M} }_{{\Omega },h,{\Phi },\lambda }^{(r)} related to polynomial compound curves.
Ali Mohammed, Katatbeh Qutaibeh
doaj +2 more sources
Marcinkiewicz Integrals on Weighted Weak Hardy Spaces [PDF]
Journal of Function Spaces, 2014 We prove that, under the condition Ω∈Lipα, Marcinkiewicz integral μΩ is bounded from weighted weak Hardy space WHwpRn to weighted weak Lebesgue space WLwpRn for maxn/n+1/2,n/n ...
Yue Hu, Yueshan Wang
doaj +2 more sources
WEIGHTED ESTIMATES FOR ROUGH PARAMETRIC MARCINKIEWICZ INTEGRALS [PDF]
Journal of the Korean Mathematical Society, 2007 Summary: We establish a weighted norm inequality for a class of rough parametric Marcinkiewicz integral operators \({\mathcal M}_\Omega^\rho\). As an application of this inequality, we obtain weighted \(L^p\) inequalities for a class of parametric Marcinkiewicz integral operators \({\mathcal M}_{\Omega,\lambda}^{*,\rho}\) and \({\mathcal M}_{\Omega,S}^\
Hussain Al-Qassem
openalex +5 more sources
Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces [PDF]
Journal of Function Spaces and Applications, 2010 In this article, we consider the Marcinkiewicz integrals with variable kernels defined by μΩ(f)(x)=(∫0∞|∫|x−y|≤tΩ(x,x−y)|x−y|n−1f(y)dy|2dtt3)1/2, where Ω(x,z)∈L∞(ℝn)×Lq(Sn−1) for q > 1.
Xiangxing Tao, Xiao Yu, Songyan Zhang
doaj +4 more sources
A NOTE ON END PROPERTIES OF MARCINKIEWICZ INTEGRAL [PDF]
Journal of the Korean Mathematical Society, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yong Ding
openalex +3 more sources
A note on Marcinkiewicz integral operators
Journal of Mathematical Analysis and Applications, 2003 Let \(\mathbb{R}^n\), \(n\geq 2\), be the \(n\)-dimensional Euclidean space and \(S^{n-1}\) be the unit sphere in \(\mathbb{R}^n\) equipped with the normalized Lebesgue measure \(d\sigma\). Let \(\Omega\) be a homogeneous function of degree 0 satisfying \(\Omega\in L^1(S^{n-1})\) and \(\int_{S^{n-1}} \Omega(y')\, d\sigma(y')= 0\), where \(y'= y/| y|\in
Al-Qassem, H.M., Al-Salman, A.J.
openaire +4 more sources
Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces
Mathematics, 2019 In this article, the boundedness of the generalized parametric Marcinkiewicz integral operators M Ω , ϕ , h , ρ ( r ) is considered. Under the condition that Ω is a function in L q ( S n - 1 ) with q &
Mohammed Ali, Oqlah Al-Refai
doaj +3 more sources
Marcinkiewicz integrals associated with Schrödinger operator and their commutators on vanishing generalized Morrey spaces [PDF]
Boundary Value Problems, 2017 Let L = − Δ + V $L=-\Delta+V$ be a Schrödinger operator, where Δ is the Laplacian on R n $\mathbb{R}^{n}$ and the non-negative potential V belongs to the reverse Hölder class RH q $\mathit{RH}_{q}$ for q ≥ n / 2 $q \ge n/2$ .
Ali Akbulut +2 more
doaj +2 more sources
Quantitative weighted L^p bounds for the Marcinkiewicz integral [PDF]
Mathematical Inequalities & Applications, 2019 Summary: Let \( \Omega\) be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and \(\mu _\Omega\) be the higher-dimensional Marcinkiewicz integral associated with \(\Omega\). In this paper, the authors proved that if \(\Omega \in L^q (S^{n-1})\) for some \(q\in (1, \infty ]\), then for \(p\in (q^\prime, \infty )\) and \
Guoen Hu, Meng Qu
openalex +3 more sources
On the LP boundedness of Marcinkiewicz integrals [PDF]
Michigan Mathematical Journal, 2002 Let \(b \in L^{\infty}(\mathbb R_{+})\) and let \(\Omega \in L^1(S^{n-1})\) with zero average where \(n \geq 2\). For a suitable mapping \(\Phi : \mathbb R^n \rightarrow \mathbb R^d\), the Marcinkiewicz integral operator \(\mu_{\Phi, \Omega, b}\) on \(\mathbb R^d\) is defined by \[ \mu_{\Phi, \Omega, b} f(x) = \Bigl( \int_0^{\infty}| F_{\Phi, t}(x) |^2
Yong Ding, Dashan Fan, Yibiao Pan
openalex +4 more sources