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On the Spaces L and W
Xianling Fan,Dun Zhao +1 more
- 01 Jan 2001
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About: The article was published on 01 Jan 2001. and is currently open access.
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Citations
Nonlinear variable exponent Picone identity and $p(x)$-sub-Laplacian first eigenvalue for general vector fields
Abimbola Abolarinwa
- 12 Sep 2022
TL;DR: In this paper , the authors established a new generalized nonlinear variable exponent Picone identity for p ( x )-sub-Laplacian, and proved uniqueness, simplicity, monotonicity and isolatedness.
An atomic decomposition of variable Besov and Triebel-Lizorkin spaces
Jingshi Xu
- 23 Feb 2009
TL;DR: An atomic decomposition of variable Besov and Triebel-Lizorkin spaces is given in this paper, where the decomposition is shown to be equivalent to the one presented in this paper.
Existence Analysis for a Model Describing Flow of an Incompressible Chemically Reacting Non-Newtonian Fluid
TL;DR: The Lipschitz approximation method is generalized and shows the existence of a weak solution provided that the minimal value of the power-law exponent is bigger than $d/2$.
Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space Lp(⋅)(logL)q(⋅)
TL;DR: In this paper, the authors studied the boundedness of Hardy-Littlewood maximal functions and applied the Hedberg's trick for Riesz potentials, and applied it to the problem of vanishing integrability.
•Dissertation
On Trace Inequalities and Compactness for Potential-type Operators
Usman Ashraf
- 01 Jan 2008
TL;DR: In this paper, the Riemann-Liouville transform with variable parameter R(x) from Lp (x) to L(x), and the measure of non-compactness of this operation is also estimated from both sides in variable exponent spaces.
References
•Book
Orlicz Spaces and Modular Spaces
Julian Musielak
- 01 Nov 1983
TL;DR: In this paper, a family of modulars depending on a parameter is described, and some applications of modular spaces are discussed, including orlicz spaces and countably modulared spaces.
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Averaging of functionals of the calculus of variations and elasticity theory
TL;DR: In this paper, the authors developed a duality method in the theory of averaging of nonlinear variational problems with stochastic Lagrangians and derived duality formulas that take account of the regularity problem.
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