Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent

By V. Kokilashvili, S. Samko. 2003

130 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c35d585f1e83f58fb5fc245f159f00992b362fa6

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In Applied Mathematics

Citations in the corpus

Operators of harmonic analysis in weighted spaces with non-standard growth (2008, unknown): “…and C.J.Neugebauer [11], L. Diening [13], [14], [15], L.Diening and M.Ruˇ z iˇ c ka [17], V. Kokilashvili, N.Samko and S.Samko [38], V.Kokilashvili and S.Samko [45], [41], [42], [43], A.Nekvinda [59], S.Samko [71], [72], [73], S.Samko, E.Shargorodsky and B.Vakulov [75] and references therein.”
Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces (2012, methodology): “For the rest of this paper, we use the lifting principle to introduce and study some new Morrey type spaces related to several Banach function spaces appeared in [4, 5, 20, 24, 25, 26, 32, 35, 41, 42, 43, 44, 47, 52, 56, 66, 67, 71, 73, 74, 75].”
THE BOUNDEDNESS OF CLASSICAL OPERATORS ON VARIABLE L p SPACES (2006, background): “[28] Kokilashvili, V., and S. Samko: Singular integrals in weighted Lebesgue spaces with variable exponent.”
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators (2005, unknown): “Samko [15,16] in the weighted case.”
Fredholmness of Singular Integral Operators with Piecewise Continuous Coefficients on Weighted Banach Function Spaces (2003, background): “The class P plays a very important role in questions on the boundedness of maximal functions and singular integrals on (weighted) Nakano spaces (see [10, 30, 46], the references therein, and also Theorem 6.”
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].”
ATOMIC DECOMPOSITION OF HARDY-MORREY SPACES WITH VARIABLE EXPONENTS (2015, background): “One of the important results in the variable exponent analysis is the identification of the class of exponent functions for which the Hardy–Littlewood maximal function is bounded on the corresponding Lebesgue spaces with variable exponent [10, 11, 13, 15, 16, 36, 38, 39, 47, 48, 49].”
Hardy inequality in variable exponent Lebesgue spaces (2007, background): “In the rapidly developing field of ”variable exponent spaces” there have already been made an essential progress in studying classical integral operators, such as maximal and singular operators, Riesz potentials and Hardy operators, we refer for example to the papers [3], [4], [5], [6], [7], [13], [”
Hardy inequality in the generalized Lebesgue spaces (2003, unknown): “We refer, for example, to the papers [1], [2], [3], [4], [14], [15], [11], [12], [10], [13], [16], [18], [19], [21] and references therein in connection with the generalized Lebesgue spaces.”
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”
Hardy's Inequality in a Variable Exponent Sobolev Space (2005, background): “After Diening’s breakthrough in the study of the Hardy-Littlewood maximal operator [1], there has been great progress in studying various potential-type operators, for the most recent advances see [2, 3, 4, 9, 12, 13].”