Results 41 to 50 of about 2,334 (153)

Boundedness of One Class of Integral Operators from Second Order Weighted Sobolev Space to Weighted Lebesgue Space

Journal of Function Spaces, 2022
In the paper, for a certain class of Hardy operators with kernels, we consider the problem of their boundedness from a second order weighted Sobolev space to a weighted Lebesgue space.
Aigerim Kalybay
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Optimal Regularity Properties of the Generalized Sobolev Spaces

Journal of Function Spaces and Applications, 2013
We prove optimal embeddings of the generalized Sobolev spaces , where is a rearrangement invariant function space, into the generalized Hölder-Zygmund space generated by a function space .
G. E. Karadzhov, Qaisar Mehmood
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QK Spaces on the Unit Circle

Journal of Function Spaces, 2014
We introduce a new space QK(∂D) of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition on K such that QK(∂D)=BMO(∂D), as well as a general criterion on weight ...
Jizhen Zhou
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Hyponormal Toeplitz Operators on the Dirichlet Spaces

Abstract and Applied Analysis, 2013
We completely characterize the hyponormality of bounded Toeplitz operators with Sobolev symbols on the Dirichlet space and the harmonic Dirichlet space.
Puyu Cui, Yufeng Lu
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Anisotropic logarithmic Sobolev inequality with a Gaussian weight and its applications

Electronic Journal of Differential Equations, 2019
In this article we prove a Logarithmic Sobolev type inequality and a Poincare type inequality for functions in the anisotropic Gaussian Sobolev space.
Filomena Feo, Gabriella Paderni
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Trudinger–Moser Inequalities in Fractional Sobolev–Slobodeckij Spaces and Multiplicity of Weak Solutions to the Fractional-Laplacian Equation

Advanced Nonlinear Studies, 2019
In line with the Trudinger–Moser inequality in the fractional Sobolev–Slobodeckij space due to [S. Iula, A note on the Moser–Trudinger inequality in Sobolev–Slobodeckij spaces in dimension one, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
Zhang Caifeng
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Sharp affine weighted L 2 Sobolev inequalities on the upper half space

Advanced Nonlinear Studies
We establish some sharp affine weighted L 2 Sobolev inequalities on the upper half space, which involves a divergent operator with degeneracy on the boundary.
Dou Jingbo, Hu Yunyun, Yue Caihui
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The Well-Posedness of Solutions for a Generalized Shallow Water Wave Equation

Abstract and Applied Analysis, 2012
A nonlinear partial differential equation containing the famous Camassa-Holm and Degasperis-Procesi equations as special cases is investigated. The Kato theorem for abstract differential equations is applied to establish the local well-posedness of ...
Shaoyong Lai, Aiyin Wang
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Existence of solutions for quasilinear parabolic equations at resonance

Electronic Journal of Differential Equations, 2013
In this article, we show the existence of nontrivial solutions for a class of quasilinear parabolic differential equations. To obtain the solution in a weighted Sobolev space, we use the Galerkin method, Brouwer's theorem, and a compact Sobolev-type ...
Gao Jia, Xiao-Juan Zhang, Li-Na Huang
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On applications of the generalized Bessel potential to solving the singular fractional Schrӧdinger equation and capacity theory

Современная математика: Фундаментальные направления
In this paper, we construct a weighted Sobolev space of fractional order based on the generalized Bessel potential. We apply these results to the analysis of the singular fractional Schrӧdinger equation.
A. L. Dzhabrailov, E. L. Shishkina
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