Abstract:
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:variable Lebesgue space, variable Sobolev space, $K$-functional, generalized modulus of continuity, direct and inverse approximation theorems, conjugate function.
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