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Oscillatory Singular Integrals with Rough Kernel
1995This paper is devoted to the study on the L p -boundedness for the oscillatory singular integral defined by $$ Tf(x) = p.v.\int_{\mathbb{R}^n } {e^{iP(x,y)} } K(x - y)f(y)dy, $$ where P(x,y) is a real polynomial on ℝ n × ℝ n , and \( K(x) = \frac{{h(\mid x\mid \Omega (x)}} {{\mid x\mid ^n }} \) with Ω ∈ Llog + L(S n−1) and h ∈ BV(ℝ+) (i.e.
Yinsheng Jiang, Shanzhen Lu
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A note concerning Marcinkiewicz integral with rough kernel
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2021In this paper, applying some properties of rough kernel and using some technical lemmas, we prove various norm inequalities concerning Marcinkiewicz integral with rough kernel. Indeed, we extend some known results on singular integrals to Marcinkiewicz integrals.
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Chapter Four. Hölder Regularity for Generalized Master Equations with Rough Kernels
, 2014We prove Hölder estimates for integro-differential equations related to some continuous time random walks. These equations are nonlocal both in space and time and recover classical parabolic equations in limit cases.
L. Caffarelli, L. Silvestre
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Fractional Calculus and Applied Analysis, 2022
Naqash Sarfraz, Muhammad Aslam
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Naqash Sarfraz, Muhammad Aslam
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Rough bilinear fractional integrals with variable kernels
Frontiers of Mathematics in China, 2010We study the rough bilinear fractional integral $$ \tilde B_{\Omega ,\alpha } (f,g)(x) = \int_{\mathbb{R}^n } {f(x + y)g(x - y)\frac{{\Omega (x,y')}} {{\left| y \right|^{n - \alpha } }}dy} , $$ , where 0 < a < n, Ω is homogeneous of degree zero on the y variable and satisfies Ω ∈ L∞(ℝn)× Ls(Sn−1) for some s ⩾ 1, and Sn−1 denotes the unit sphere ...
Dashan Fan, Jiecheng Chen
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On the mixed radial-angular integrability of Marcinkiewicz integrals with rough kernels
, 2021Ronghui Liu, Feng Liu, Huo-xiong Wu
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Rough Cluster Algorithm Based on Kernel Function
2008By means of analyzing kernel clustering algorithm and rough set theory, a novel clustering algorithm, rough kernel k-means clustering algorithm, was proposed for clustering analysis. Through using Mercer kernel functions, samples in the original space were mapped into a highdimensional feature space, which the difference among these samples in sample ...
Yanning Zhang +4 more
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Rough Kernel Clustering Algorithm with Adaptive Parameters
2011Through analyzing kernel clustering algorithm and rough set theory, a novel clustering algorithm, Rough kernel k-means clustering algorithm with adaptive parameters, is proposed for clustering analysis in this paper. By using Mercer kernel functions, we can map the data in the original space to a highdimensional feature space, in which we can use rough
Tao Zhou +4 more
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Boundedness of Multilinear Commutators with Rough Kernels on Morrey-Herz Spaces
, 2013This paper is concerning the commutators generated by the multilinear singular integral with rough kernels and BMO functions. The boundedness of the multilinear commutators Tb(f) is established on the Morrey-Herz space by using the JohnNirenberg ...
Qiaoni, Li, Shuangping, Tao
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On a Class of Singular Integral Operators With Rough Kernels
Canadian Mathematical Bulletin, 2006AbstractIn 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.
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