Maximal and Fractional Operators in Weighted $L^{p(x)}$ Spaces

By V. Kokilashvili, S. Samko. 2004

171 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c490078f4ef92e8ab50cbb39d2cf2ac27100d73e

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

MAXIMAL FUNCTIONS IN VARIABLE EXPONENT SPACES: LIMITING CASES OF THE EXPONENT (2009, background): “[7, 12, 17, 29, 31], with related differential equations [1, 3, 15, 16, 32, 41, 42], and with applications [4, 38].”
Hardy inequality in the generalized Lebesgue spaces (2003, background): “The boundedness statement of Theorem A adjoins to weighted variable exponent estimates obtained in [14], see also [10] and [11].”
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators (2005, background): “Samko [17], limiting equalities for bounded domains having been recently proved in S.”
Boundedness of Maximal and Singular Operators in Morrey Spaces with Variable Exponent (2008, methodology): “For mapping properties of maximal functions and singular integrals on Lebesgue spaces with variable exponent we refer to [9], [10], [7], [6], [19]-[20], [26], [13] (see also [29], [17] and references therein).”
Hardy's Inequality in a Variable Exponent Sobolev Space (2005, background): “Our proof is different from that in [13].”
The maximal operator on weighted variable Lebesgue spaces (2011, result): “) The first results of this kind we proved by Kokilashvili, Samko and their collaborators [25, 40, 41, 42, 43]; these results were more recently extended to classes of weights who oscillate between powers: see [1, 21, 22, 23, 24, 26, 27, 37, 38].”
Sobolev embeddings in metric measure spaces with variable dimension (2006, background): “[1,3,6,17,24,25], and some studies in the metric space setting have also appeared [12,18–20,27].”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, methodology): “4) is satisfied, while boundedness results in L for fractional maximal-type operators have been obtained by Kokilashvili & Samko [196]; see also [85] for more on Harmonic Analysis in L-spaces.”