Geodesic
Approximation of functions and their conjugates in variable Lebesgue spaces
Sbornik. Mathematics, Tome 208 (2017) no. 1, pp. 44-59

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One-sided Steklov means are used to introduce moduli of continuity of natural order in variable $L^{p(\cdot)}_{2\pi}$-spaces. A direct theorem of Jackson-Stechkin type and an inverse theorem of Salem-Stechkin type are given. Similar results are obtained for the conjugate functions. Bibliography: 24 titles.
Keywords: $K$-functional, generalized modulus of continuity, direct and inverse approximation theorems, conjugate function.
Mots-clés : variable Lebesgue space, variable Sobolev space 
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S. S. Volosivets. Approximation of functions and their conjugates in variable Lebesgue spaces. Sbornik. Mathematics, Tome 208 (2017) no. 1, pp. 44-59. http://geodesic.mathdoc.fr/item/SM_2017_208_1_a1/