On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators

By S. Samko. 2005

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On Direct And Inverse Theorems Of Approximation Theory In Variable Lebesgue And Sobolev Spaces (2013, methodology): “The properties of singular integrals in the spaces L p(x) μ (E)) were studied in [18][25] under the same logarithmic DiniLipschitz condition on the variable exponent p(x).”
The maximal operator on weighted variable Lebesgue spaces (2011, background): “Dedicated to Prof. Stefan Samko on the occasion of his 70th Anniversary We study the boundedness of the maximal operator on the weighted variable exponent Lebesgue spaces Lp(·)ω (Ω).”
FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, background): “Samko [189], and, a book; Diening, Harjulehto, Hästö and Růžička [40].”
Fractional integration and differentiation of variable order: an overview (2012, background): “We also refer to the paper [51], where the reader”
Sobolev inequalities with variable exponent attaining the values $1$ and $n$ (2008, background): “Introduction Variable exponent spaces have been studied in many articles over the past decade; for surveys see [10], [27].”
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], [”