共查询到20条相似文献,搜索用时 15 毫秒
1.
Humberto Rafeiro Stefan Samko 《Journal of Mathematical Analysis and Applications》2010,365(2):483-497
Under the standard assumptions on the variable exponent p(x) (log- and decay conditions), we give a characterization of the variable exponent Bessel potential space Bα[Lp(⋅)(Rn)] in terms of the rate of convergence of the Poisson semigroup Pt. We show that the existence of the Riesz fractional derivative Dαf in the space Lp(⋅)(Rn) is equivalent to the existence of the limit . In the pre-limiting case we show that the Bessel potential space is characterized by the condition ‖α(I−Pε)f‖p(⋅)≦Cεα. 相似文献
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In this paper, we introduce a new class of weights Ap (Rn) which retains many fine properties of the classical Muchenhoupt weights Ap (Rn). While Ap (Rn) is too big a class to obtain the weighted norm inequalities for rough singular integrals and Marcinkiewicz integrals, our new class Ap (Rn) adapts well to these rough operators. As applications, we improve some known weighted estimates. 相似文献
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主要研究了带参数的抛物型Marcinkiewicz函数μσΩ,h(f)的L2((R)n)有界性,用核的分解技术和Fourier变换估计的方法分别在当1<-γ<∞,h∈Hγ'(IR)+),Ω∈L(logL)1/γ(Sn-1)条件下和当1〈γ≤∞,h∈△γ((IR)+),Ω∈Llog+L(Sn-1)条件下,建立了μσΩ,h(f)的L2((R)n)有界性,并推广了以前学者的结论. 相似文献
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Wenming Li 《Journal of Mathematical Analysis and Applications》2006,322(2):1215-1223
We give a condition which is sufficient for the two-weight (p,q) inequalities for commutators of potential type integral operators. 相似文献
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In this paper, the authors consider the boundedness of generalized higher commutator of Marcinkiewicz integral μΩ^b, multilinear Marcinkiewicz integral μΩ^A and its variation μΩ^A on Herz-type Hardy spaces, here Ω is homogeneous of degree zero and satisfies a class of L^s-Dini condition. And as a special case, they also get the boundedness of commutators of Marcinkiewicz integrals on Herz-type Hardy spaces. 相似文献
6.
Wenming Li 《Mathematische Nachrichten》2008,281(6):839-846
We give a condition which is sufficient for the two‐weight (p, q) inequalities for multilinear potential type integral operators, where 1 < p ≤ q < ∞. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Bukhgeim A. L. Dyatlov G. V. Kardakov V. B. Tantserev E. V. 《Siberian Mathematical Journal》2004,45(4):618-627
We consider an inverse problem for the stationary elasticity system with constant Lame coefficients and a variable matrix coefficient depending on the spatial variables and frequency. The right-hand side contains a delta-function whose support (source) varies in some domain disjoint from the support of the variable coefficient. The inverse problem is to find the coefficient from the scattered wave measured at the same point at which the perturbation originates. A uniqueness theorem is proven. The proof bases on reduction of the inverse problem to a family of equations with the M. Riesz potential. 相似文献
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In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with the usual one. 相似文献
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In this paper, we prove the Triebel-Lizorkin boundedness for the Marcinkiewicz integral with rough kernel. The method we apply here enables us to consider more general operators. 相似文献
11.
Dong-Myung Lee Jung-Gon Lee Sun-Ho Yoon 《Proceedings of the American Mathematical Society》2002,130(12):3555-3563
In this paper we present a versatile construction of multiresolution analysis of two variables by means of eigenvalue problems of the integral equation, for . As a consequence we show that if is the solution of the equation with , then constructs a two-variable multiresolution analysis.
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证明一类带粗糙核平方函数的加权及l~r-向量值不等式,其中所用的权函数为径向权.作为推论,我们得出了带H~1-核的Marcinkiewicz积分μ_Ω的相应不等式. 相似文献
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本文研究了紧致齐性空间上的Riesz位势算子与Bessel位势算子,Riesz变换与Bessel变换,给出了上述算子对应的核函数的具体构造并证明了Riesz变换与Bessel变换作为奇异积分算子的H ̄p有界性,p>0。 相似文献
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In this paper the authors give a new integral estimate of the Bessel function,which is an extension of Calder(?)n-Zygmund's result.As an application of this result,we prove that the parameterized Marcinkiewicz integralμ_Ω~p with variable kernels is of type (2,2),where the kernel functionΩdoes not have any smoothness on the unit sphere in R~n. 相似文献
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Finite element wavelets with improved quantitative properties 总被引:1,自引:0,他引:1
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In this paper, the authors prove the boundedness of the multilinear maximal functions, multilinear singular integrals and multilinear Riesz potential on the product generalized Morrey spaces Mp1,ω1(Rn) ×···× Mpm,ω1(Rn) respectivelyThe main theorems of this paper extend some known results. 相似文献
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本文研究了Marcinkiewicz积分μΩ的有界性的问题,借助Ap权的性质,得到了相应与Littlewood-Paley g-函数的Marcinkiewica积分算子μΩ的(Lp(v),Lp(u))有界性,并且证明了相应于Littlewood-Paley gλ*-函数和Lusin面积积分的Marcinkiewicz积分μ*Ω,λ,μΩ,S的(Lp(v),Lp(u))有界性. 相似文献
20.
Marcinkiewicz积分交换子的有界性 总被引:8,自引:0,他引:8
本文考虑了Marcinkiewicz积分交换子μΩb在Lp(Rn)和Hardy空间的有界性, 其中Ω∈L1(Sn-1)是Rn中的零次齐次函数且满足一类Lq-Dini条件,因此改进了以往的结果. 相似文献