Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp(·) and Wk,p(·)

By Lars Diening. 2004

345 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a8a081c8ec0c845365a7b92caf0d636b75d03fea

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications (2008, neutral): “5 of [10] it follows that W 1,p(·) 0 (Ω) embeds compactly into L p(·)(Ω).”
The obstacle problem for nonlinear elliptic equations with variable growth and L1-data (2008, neutral): “deﬁne W−1,p′(·)(Ω) as the dual space 6 of W1,p(·) 0 (Ω), where Poincar´e’s inequality is also valid. Besides, the Sobolev embedding W1,p(·) 0 (Ω) → Lp ∗(·)(Ω) , p∗(·) = Np(·) N−p(·) still holds (see [18, 16, 20]). Let us ﬁnally introduce the following notation: given two bounded measurable functions”
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators (2005, background): “Diening [6], in [6] there being also treated the ca unbounded domains under the assumption that the maximal operator is bounded version of the Sobolev-type theorem for unbounded domain was given in V.”
Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space Lp(⋅)(logL)q(⋅) (2008, positive): “¤ By applying the boundedness of the maximal operator and Hedberg’s trick [20], we establish the Sobolev type inequality for Riesz potentials, as an extension of the authors [27, Theorem 3.5] (see also Almeida-Samko [3], Diening [6], Futamura-Mizuta [10], Futamura-Mizuta-Shimomura [11, 12], Harjuleh”
Sobolev’s inequality for double phase functionals with variable exponents (2018, background): “For variable exponent Lebesgue spaces Lp( ⋅ ), Sobolev’s inequality was studied in [6, 9, 10], etc.”
Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces (2012, background): “The variable exponent analysis recently gains a lot of attentions [4, 5, 14, 15, 17, 18, 19, 20, 21, 36, 41, 44, 49, 50, 57, 75] because the boundedness of several important linear operators in analysis, especially, the Hardy–Littlewood maximal operator, can be established for the variable Lebesgue ”