共查询到20条相似文献,搜索用时 822 毫秒
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We give conditions for the convergence of approximate identities, both pointwise and in norm, in variable L p spaces. We unify and extend results due to Diening [8], Samko [18] and Sharapudinov [19]. As applications, we give criteria for smooth functions to be dense in the variable Sobolev spaces, and we give solutions of the Laplace equation and the heat equation with boundary values in the variable L p spaces. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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本文给出了一些关于变指数加权Sobolev空间拟连续性的精确刻画. 进而在拟连续的意义下得到变指数加权Sobolev空间唯一性结果. 相似文献
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Kwok-Pun Ho 《Integral Transforms and Special Functions》2018,29(3):207-220
We establish the vector-valued inequalities of the Ahlfors–Beurling operator on Morrey spaces with variable exponents. As consequences of these inequalities, we have the boundedness of the Ahlfors–Beurling transform on Lebesgue spaces with variable exponents and Morrey spaces. The results obtained in this paper are new in the case of Morrey spaces. 相似文献
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In this paper, we consider the 2-D nonhomogeneous incompressible magnetohydrodynamic equations with variable viscosity and variable conductivity. We obtain the global existence of solutions for this system with initial data in the scaling invariant Besov spaces and without size restriction for the initial velocity and magnetic field. 相似文献
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本文研究了带有一个可变参数的四阶奇异边值问题,利用Banach空间的不动点理论,在非常弱的条件下,获得了带可变参数四阶奇异边值问题存在正解的结果. 相似文献
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研究对偶Toeplitz算子(半)交换时其符号的关系.通过对其符号的分解,借助多复变函数的有关理论,得到了单位球Dirichlet空间上以多重调和函数为符号的对偶Toeplitz算子Sψ与Sψ(半)交换的充要条件. 相似文献
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In this paper, we initiate the study of the method of upper and lower solutions and monotone iterative technique for impulsive differential equations with variable moments. Because of the difficult nature of the problem, we shall restrict ourselves to a simple situation which, as we shall see, presents enough complications. 相似文献
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The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with variable exponent.Based on this main purpose, we first characterize the Triebel-Lizorkin spaces with variable exponent by two families of operators. Immediately after, applying the characterizations of TriebelLizorkin space with variable exponent, we obtain that b ∈■β if and only if the commutator of Calderón-Zygmund singular integral operator is bounded, respectively, from■ to■,from■ to■ with■. Moreover, we prove that the commutator of Riesz potential operator also has corresponding results. 相似文献
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本文研究了一类次线性算子T和BMO(X)函数b生成的交换子[b,T]的有界性质.利用函数分解方法,获得了[b,T]在WMK˙pα,,qλ(X)上的有界性结果. 相似文献
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In this article we study metric measure spaces with variable dimension. We consider Lebesgue spaces on these sets, and embeddings
of the Riesz potential in these spaces. We also investigate Hajłasz-type Sobolev spaces, and prove Sobolev and Trudinger inequalities
with optimal exponents. All of these questions lead naturally to function spaces with variable exponents.
Supported the Research Council of Norway, Project 160192/V30. 相似文献
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María Emilia Caballero Begoña Fernández David Nualart 《Journal of Theoretical Probability》1998,11(3):831-851
In this paper we show some estimates for the density of a random variable on the Wiener space that satisfies a nondegeneracy condition using the stochastic calculus of variations. The case of a diffusion process is considered, and an application to the solution of a stochastic partial differential equation is discussed. 相似文献
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Petteri Harjulehto Peter Hästö Mika Koskenoja Susanna Varonen 《Potential Analysis》2006,25(3):205-222
We define and study variable exponent Sobolev spaces with zero boundary values. This allows us to prove that the Dirichlet energy integral has a minimizer in the variable exponent case. Our results are based on a Poincaré-type inequality, which we prove under a certain local jump condition for the variable exponent. 相似文献
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该文在随机元阵列随机有界于某非负随机变量的条件下,进一步讨论了完全收敛性与Banach空间p型性质的等价性. 相似文献
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We prove the boundedness for a class of multi-sublinear singular integral operators on the product of central Morrey spaces with variable exponents. Based on this result, we obtain the boundedness for the multilinear singular integral operators and two kinds of multilinear singular integral commutators on the above spaces. 相似文献
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In this article we introduce Besov spaces with variable smoothness and integrability indices. We prove independence of the choice of basis functions, as well as several other basic properties. We also give Sobolev-type embeddings, and show that our scale contains variable order Hölder-Zygmund spaces as special cases. We provide an alternative characterization of the Besov space using approximations by analytic functions. 相似文献
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In [4], a new family W(L^p(x), Lm^q) of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space L^p(x) (R) and the global component is a weighted Lebesgue space Lm^q (R). This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality W (L^p(x), Lm^q) = L^q (R). Later we give some characterization of Wiener amalgam space W (L^p(x), Lm^q).In Section 3 we define the Wiener amalgam space W (FL^p(x), Lm^q) and investigate some properties of this space, where FL^p(x) is the image of L^p(x) under the Fourier transform. In Section 4, we discuss boundedness of the Hardy- Littlewood maximal operator between some Wiener amalgam spaces. 相似文献
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Let S be the multiplication operator by an independent variable x in L
2(0,1), and let V be an integral operator of Volterra type. In this note, we find sufficient conditions for the similarity of the operators T := S + V and S and discuss some generalizations to an abstract setting of the results obtained. 相似文献