Results 21 to 30 of about 38,177 (303)
A singular integral operator with rough kernel [PDF]
Proceedings of the American Mathematical Society, 1997 Let b(y) be a bounded radial function and Q(y') an H1 function on the unit sphere satisfying the mean zero property. Under certain growth conditions on 4(t), we prove that the singular integral operator T-,bf (X) = p.v. j f (x y(jy)y)b(y)yIl-nQ(y') dy is bounded in LP(RI) for 1 < p < oo.
Dashan Fan, Yibiao Pan
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A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution
Mathematics, 2022 In this article, certain sharp Lp estimates for a specific class of generalized Marcinkiewicz operators with mixed homogeneity associated to surfaces of revolution are established.
Mohammed Ali, Hussain Al-Qassem
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On maximal and potential operators with rough kernels in variable exponent spaces [PDF]
, 2016 In the framework of variable exponent Lebesgue and Morrey spaces we prove some boundedness results for operators with rough kernels, such as the maximal operator, fractional maximal operator, sharp maximal operators and fractional operators. The approach
Rafeiro, Humberto, Samko, Stefan
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Integral operators with rough kernels in variable Lebesgue spaces [PDF]
Acta Mathematica Hungarica, 2020 In this paper we study integral operators with kernels \begin{equation*} K(x,y)= k_1( x- A_1y)...k_m( x-A_my), \end{equation*} $k_i(x)=\frac{ _i(x)}{|x|^{n/q_i}}$ where $ _i: \mathbb{R}^n\to \mathbb{R}$ are homogeneous functions of degree zero, satisfying a size and a Dini condition, $A_{i}$ are certain invertible matrices, and $\frac n{q_1}+\dots ...
Urciuolo, Marta +1 more
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Operators with rough singular kernels
Journal of Mathematical Analysis and Applications, 2008 AbstractFor α>0, we study the singular integral operators TΩ,α and the Marcinkiewicz integral operator μΩ,α. The kernels of these operators behave like |y|−n−α near y=0, and contain a distribution Ω on the unit sphere Sn−1. We prove that if Ω∈Hr(Sn−1) (r=(n−1)/(n−1+α)) satisfying certain cancellation condition, then both TΩ,α and μΩ,α can be extend to ...
Dashan Fan +3 more
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A Note on Marcinkiewicz Integrals along Submanifolds of Finite Type
Journal of Function Spaces, 2018 We study the parametric Marcinkiewicz integrals along submanifolds of finite type with rough kernels. The kernels of our operators are allowed to be very rough both on the unit sphere and in the radial direction. Under the rather weakened size conditions
Daiqing Zhang
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Advances in Nonlinear Analysis, 2021 This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces.
Zhang Xiao, Liu Feng, Zhang Huiyun
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On commutators of Marcinkiewicz integrals with rough kernel
Journal of Mathematical Analysis and Applications, 2002 AbstractIn this note we prove that the higher-order commutators μmΩ,b, μ∗,mΩ,λ,b and μmΩ,S,b are all of bounded operators on the weighted Lp spaces. These commutators are formed respectively by a BMO(Rn) function b(x) and a class of rough Marcinkiewicz integral operators μΩ, μ∗Ω,λ and μΩ,S, which are corresponding to the Littlewood–Paley g-function ...
Kôzô Yabuta, Yong Ding, Shanzhen Lu
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Journal of Inequalities and Applications, 2007 We give the L2 estimates for the Marcinkiewicz integral with rough variable kernels associated to surfaces. More precisely, we give some other sufficient conditions which are different from the conditions known before to warrant that the L2-boundedness ...
Kôzô Yabuta, Qingying Xue
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Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains
Axioms, 2023 We prove Lp estimates of a class of generalized Marcinkiewicz integral operators with mixed homogeneity on product domains. By using these estimates along with an extrapolation argument, we obtain the boundedness of our operators under very weak ...
Mohammed Ali, Hussain Al-Qassem
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