On Sobolev Theorem for Riesz-Type Potentials in Lebesgue Spaces with Variable Exponent

By V. Kokilashvili, S. Samko. 2003

104 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/33e2665d0b03cd4b605d34744ae61d7e4599331d

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In Applied Mathematics

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Citations in the corpus

Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators (2005, unknown): “Some version of the Sobolev-type theorem for unbounded domain was given in V. Kokilashvili and S. Samko [ 14 ].”
Sobolev embeddings for variable exponent riesz potentials on metric spaces (2006, methodology): “As an application of the boundedness of maximal functions, we establish Sobolev’s embedding theorem for variable exponent Riesz potentials on metric space; in the case a1 = 0, see also Diening [4] and Kokilashvili–Samko [17], [18], In the borderline case of Sobolev’s theorem, we are concerned with e”
Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space Lp(⋅)(logL)q(⋅) (2008, unknown): “8 below) is given in Section 2, which is an extension of Almeida-Samko [3], Diening [6], Futamura-Mizuta [10], Futamura-Mizuta-Shimomura [11, 12], Harjulehto-HästöPere [18], Kokilashvili-Samko [21], Mizuta-Shimomura [27] and Samko-Vakulov [31].”
Characterization of Riesz and Bessel potentials on variable Lebesgue spaces (2006, methodology): “Some weighted version of the Sobolev theorem for R with the power weight fixed to infinity, was obtained in [14].”
On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators (2005, background): “Another version of the Sobolev theorem for the space Rn was proved in refs. [ 84 , 85] for the”
THE BOUNDEDNESS OF CLASSICAL OPERATORS ON VARIABLE L p SPACES (2006, methodology): “Kokilashvili and Samko [29] proved it on R with L · ) replaced by a certain weighted variable L space.”
Sobolev embeddings in metric measure spaces with variable dimension (2006, background): “variable exponent setting have to been studied for instance in [5, 12, 23 , 28].”
The fractional maximal operator and fractional integrals on variable $L^p$ spaces (2007, background): “Recently, Kokilashvili and Samko [19] proved norm inequalities for a variable fractional maximal operator, with the constant α replaced by a function α(·).”
Sobolev inequalities with variable exponent attaining the values $1$ and $n$ (2008, background): “, in [1, 2, 4, 6, 8, 10, 11, 12, 13, 15, 16, 20, 24, 28] in the variable exponent setting.”