Results 41 to 50 of about 4,761,041 (315)
, 2013 In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the
A. Berlinet +19 more
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Final State Problem for the Dirac-Klein-Gordon Equations in Two Space Dimensions
Abstract and Applied Analysis, 2013 We study the final state problem for the Dirac-Klein-Gordon equations (DKG) in two space dimensions. We prove that if the nonresonance mass condition is satisfied, then the wave operator for DKG is well defined from a neighborhood at the origin in lower ...
Masahiro Ikeda
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Multivariate box spline wavelets in higher-dimensional Sobolev spaces
Journal of Inequalities and Applications, 2018 We construct wavelets and derive a density condition of MRA in a higher-dimensional Sobolev space. We give necessary and sufficient conditions for orthonormality of wavelets in Hs(Rd) $H^{s}(\mathbb {R}^{d})$.
Raj Kumar, Manish Chauhan
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On three-dimensional Hall-magnetohydrodynamic equations with partial dissipation
Boundary Value Problems, 2022 In this paper, we address the Hall-MHD equations with partial dissipation. Applying some important inequalities (such as the logarithmic Sobolev inequality using BMO space, bilinear estimates in BMO space, Young’s inequality, cancellation property ...
Baoying Du
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Dual Toeplitz Operators on the Orthogonal Complement of the Fock–Sobolev Space
Journal of Mathematics, 2023 In this paper, we consider the dual Toeplitz operators on the orthogonal complement of the Fock–Sobolev space and characterize their boundedness and compactness.
Li He, Biqian Wu
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Weighted Variable Sobolev Spaces and Capacity
Journal of Function Spaces and Applications, 2012 We define weighted variable Sobolev capacity and discuss properties of capacity in the space 𝑊1,𝑝(⋅)(ℝ𝑛,𝑤). We investigate the role of capacity in the pointwise definition of functions in this space if the Hardy-Littlewood maximal operator is bounded on ...
Ismail Aydin
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An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces
Advances in Nonlinear Analysis, 2020 It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate.
Martínez Ángel D., Spector Daniel
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INVERSE SPECTRAL PROBLEMS FOR STURM–LIOUVILLE OPERATORS WITH SINGULAR POTENTIALS. IV. POTENTIALS IN THE SOBOLEV SPACE SCALE [PDF]
Proceedings of the Edinburgh Mathematical Society, 2004 We solve the inverse spectral problems for the class of Sturm–Liouville operators with singular real-valued potentials from the Sobolev space $W^{s-1}_2(0,1)$, $s\in[0,1]$.
R. Hryniv, Y. Mykytyuk
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Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets
, 2015 We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space equipped with a doubling measure supporting a p-Poincar\'e inequality with ...
Björn, Anders +2 more
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Journal of Mathematical Analysis and Applications, 2011 AbstractFix strictly increasing right continuous functions with left limits and periodic increments, Wi:R→R, i=1,…,d, and let W(x)=∑i=1dWi(xi) for x∈Rd. We construct the W-Sobolev spaces, which consist of functions f having weak generalized gradients ∇Wf=(∂W1f,…,∂Wdf).
Alexandre B. Simas, Fábio J. Valentim
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