共查询到20条相似文献,搜索用时 31 毫秒
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Rovshan A. Bandaliev 《Czechoslovak Mathematical Journal》2013,63(4):1149-1152
In this paper the author proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with variable exponent. As an application he proved the boundedness of certain sublinear operators on the weighted variable Lebesgue space. The proof of the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent does not contain any mistakes. But in the proof of the boundedness of certain sublinear operators on the weighted variable Lebesgue space Georgian colleagues discovered a small but significant error in my paper, which was published as R.A.Bandaliev, The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces, Czech. Math. J. 60 (2010), 327–337. 相似文献
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In this paper, we obtain the necessary and sufficient condition of the pre-compact sets in the variable exponent Lebesgue spaces, which is also called the Riesz-Kolmogorov theorem. The main novelty appearing in this approach is the constructive approximation which does not rely on the boundedness of the Hardy-Littlewood maximal operator in the considered spaces such that we do not need the log-H¨older continuous conditions on the variable exponent. As applications, we establish the boundedness of Riemann-Liouville integral operators and prove the compactness of truncated Riemann-Liouville integral operators in the variable exponent Lebesgue spaces. Moreover, applying the Riesz-Kolmogorov theorem established in this paper, we obtain the existence and the uniqueness of solutions to a Cauchy type problem for fractional differential equations in variable exponent Lebesgue spaces. 相似文献
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Rovshan A. Bandaliev 《Czechoslovak Mathematical Journal》2010,60(2):327-337
The main purpose of this paper is to prove the boundedness of the multidimensional Hardy type operator in weighted Lebesgue
spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted
variable Lebesgue space. 相似文献
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We study two-weight inequalities with general-type weights for Hardy-Littlewood maximal operator in the Lebesgue spaces with
variable exponent. The exponent function satisfies log-Holder-type local continuity condition and decay condition in infinity.
The right-hand side weight to the certain power satisfies the doubling condition. Sawyer-type two-weight criteria for fractional
maximal functions are derived. 相似文献
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R. A. Bandaliev 《Lithuanian Mathematical Journal》2010,50(3):249-259
The main purpose of this paper is to prove a two-weight criterion for the multidimensional Hardy-type operator in weighted
Lebesgue spaces with variable exponent. As an application, we prove the boundedness of Riesz potential and fractional maximal
operators on the weighted variable Lebesgue space. 相似文献
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Poincaré and Sobolev Inequalities for Vector Fields Satisfying Hrmander's Condition in Variable Exponent Sobolev Spaces
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In this paper,we will establish Poincare inequalities in variable exponent non-isotropic Sobolev spaces.The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebesgue spaces on spaces of homogeneous type.We obtain the first order Poincare inequalities for vector fields satisfying Hrmander's condition in variable non-isotropic Sobolev spaces.We also set up the higher order Poincare inequalities with variable exponents on stratified Lie groups.Moreover,we get the Sobolev inequalities in variable exponent Sobolev spaces on whole stratified Lie groups.These inequalities are important and basic tools in studying nonlinear subelliptic PDEs with variable exponents such as the p(x)-subLaplacian.Our results are only stated and proved for vector fields satisfying Hrmander's condition,but they also hold for Grushin vector fields as well with obvious modifications. 相似文献
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A. Fiorenza A. Gogatishvili T. Kopaliani 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2014,49(5):232-240
In this paper we study some estimates of norms in variable exponent Lebesgue spaces for singular integral operators that are imaginary powers of the Laplace operator in ? n . Using the Mellin transform argument, fromthese estimates we obtain the boundedness for a family of maximal operators in variable exponent Lebesgue spaces, which are closely related to the (weak) solution of the wave equation. 相似文献
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A class of anisotropic Herz-type Hardy spaces with variable exponent associated with a non-isotropic dilation on \({\mathbb{R}^{n}}\) are introduced, and characterizations of these spaces are established in terms of atomic and molecular decompositions. As some applications of the decomposition theory, the authors study the interpolation problem and the boundedness of a linear operator on the anisotropic Herz-type Hardy spaces with variable exponent. 相似文献
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Jing-shi Xu 《Czechoslovak Mathematical Journal》2007,57(1):13-27
The boundednees of multilinear commutators of Calderón-Zygmund singular integrals on Lebesgue spaces with variable exponent
is obtained. The multilinear commutators of generalized Hardy-Littlewood maximal operator are also considered. 相似文献
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Osvaldo Gorosito Gladis Pradolini Oscar Salinas 《Czechoslovak Mathematical Journal》2010,60(4):1007-1023
In the context of variable exponent Lebesgue spaces equipped with a lower Ahlfors measure we obtain weighted norm inequalities
over bounded domains for the centered fractional maximal function and the fractional integral operator. 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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On Regularization of a Source Identification Problem in a Parabolic PDE and its Finite Dimensional Analysis
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Subhankar Mondal & M. Thamban Nair 《偏微分方程(英文版)》2021,34(3):240-257
We consider the inverse problem of identifying a general source term, which is a function of both time variable and the spatial variable, in a parabolic PDE from the knowledge of boundary measurements of the solution on some portion of the lateral boundary. We transform this inverse problem into a problem of solving a compact linear operator equation. For the regularization of the operator equation with noisy data, we employ the standard Tikhonov regularization, and its finite dimensional realization is done using a discretization procedure involving the space $L^2(0,\tau;L^2(Ω))$. For illustrating the specification of an a priori source condition, we have explicitly obtained the range space of the adjoint of the operator involved in the operator equation. 相似文献
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Petteri Harjulehto Peter H?st? Yoshihiro Mizuta Tetsu Shimomura 《manuscripta mathematica》2011,135(3-4):381-399
In this paper we study the iterated Hardy?CLittlewood maximal operator in variable exponent Lebesgue spaces with exponent allowed to reach the value 1. We use modulars where the L p(·)-modular is perturbed by a logarithmic-type function, and the results hold also in the more general context of such Musielak?COrlicz spaces. 相似文献
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In the case of Ω∈ Lipγ(Sn-1)(0 γ≤ 1), we prove the boundedness of the Marcinkiewicz integral operator μΩon the variable exponent Herz-Morrey spaces. Also, we prove the boundedness of the higher order commutators μmΩ,bwith b ∈ BMO(Rn) on both variable exponent Herz spaces and Herz-Morrey spaces, and extend some known results. 相似文献
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In a weighted Sobolev-type space, the well-posedness and unique solvability of a problem without initial conditions for a third-order operator-differential equation with an inverse parabolic principal part are established. The solvability conditions are expressed in terms of the operator coefficients of the equation. Additionally, the norms of the operators of intermediate derivatives closely related to the solvability conditions are estimated. The relation between the weight exponent and the lower boundary of the spectrum of the basic operator involved in the principal part of the equation is established. Note that the principal part of the equation has a multiple characteristic. 相似文献
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