On the Spaces L and W

By Xianling Fan, Dun Zhao. 2001

522 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/79878b000e9402ccbe1c6d7d1ed438ea72eee440

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Citations in the corpus

Quasilinear elliptic problems with nonstandard growth. (2011, background): “Samko [16, 17, 18] working based on earlier Russian work (Sharapudinov [19] and Zhikov [20]), Fan and collaborators [5, 6, 7, 8] drawing inspiration from the study of differential equations(e.”
On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators (2005, methodology): “We refer to the papers by Kovácǐk and Rákosnǐk [30], Samko [31, 35] and Fan and Zhao [32] for the proofs of the main results on the generalized Lebesgue spaces, but give the main definitions for the reader’s convenience.”
Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation (2017, background): “But the modern theory of function spaces with variable exponents was started with the articles [45] of Kováčik and Rákosnı́k and [32] of Fan and Zhao as well as [21] of Cruz-Uribe and [24] of Diening, and nowadays has been widely used in harmonic analysis (see, for example, [22, 25, 79]).”
Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)-Laplacian (2013, methodology): “4 [12] In W 1,p x ð Þ 0 ð Þ the Poincaré inequality holds, that is, there exists a positive constant C0 such that”
Multiple solutions for a class of p(x)-Laplacian equations in involving the critical exponent (2010, background): “For a deeper treatment of these spaces, we refer to [4, 5, 7, 8, 10].”
Multiple solutions for a p(x)-Kirchhoff-type equation with sign-changing nonlinearities (2013, background): “[25,26] and the lecture notes by Diening et al.”
An atomic decomposition of variable Besov and Triebel-Lizorkin spaces (2009, background): “Moreover, these spaces have been applied to partial differential equations and the calculus of variation, see [1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 16, 17, 18, 19, 21, 22, 29] and references therein.”
Operators of harmonic analysis in weighted spaces with non-standard growth (2008, unknown): “By the Riesz theorem, valid for the spaces with variable exponent in the case 1 < p− ≤ p+ < ∞, (see [46], [70]), we have ‖f‖0 L q(·) ̺ = ‖f q̺q‖Le q(·) ≤ sup ∫”
FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, background): “This is initially considered by [101] and independently investigated to [49].”
The concentration-compactness principle for variable exponent spaces and applications (2009, unknown): “The following proposition is also proved in [9] and it will be most usefull.”
Characterization of Riesz and Bessel potentials on variable Lebesgue spaces (2006, background): “We refer to the papers [16], [27], where the basics of such spaces were developed, to the papers [9], [23], where the denseness of nice functions in Sobolev variable spaces was considered, and to the papers [3], [5], [7], [8], [13], [15],[18], [21], [22] and the recent preprints [2], [4] and referen”
Atomic, molecular and wavelet decomposition of 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability (2010, background): “A very good resource is [23] for more details.”
Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space Lp(⋅)(logL)q(⋅) (2008, background): “In recent years, the generalized Lebesgue spaces have attracted more and more attention, in connection with the study of elasticity, fluid mechanics and differential equations with p(·)-growth; see for example Orlicz [29], Kováčik-Rákosńık [22], Edmunds-Rákosńık [7] and R ◦ užička [30].”
Existence and multiplicity results for a newp(x)-Kirchhoff problem (2019, background): “The following results were proved in [18].”
Some remarks on the Hardy-Littlewood maximal function on variable Lp spaces (2005, unknown): “, [9]) that if p− > 1 and p+ < ∞, then the following Hölder inequality ∫”
Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent (2003, background): “2 is well known in the case of constant exponent, in the case of variable exponent and ρ(x) ≡ 1 it was proved in [17].”