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• W208007606 abstract "We consider the Lebesgue space L p(x) 2 π with variable exponent p(x). It consist of measurable functions f(x) for which the integral ∫ 0 2 π |f(x)| p(x) dx exist. We establish an analogue Jackson's second theorem in the case when the 2 π -periodic variable exponent p(x) ≥ 1 satisfies the condition |p(x) - p(y)| · ln(2 π )/(|x - y|) ≤ d, x,y ∈ [0,2 π ]. Results obtained in present paper radically differ from other authors results on this subject because we don't require from variable exponent p(x) the fulfillment of additional condition p(x) ≥ π which is closely related with boundedness of Hardy - Littlewood maximal function M(f) in L p(x) 2 π . In the definition of the modulus of continuity of a function f(x) ∈ L 2 π p(x) , we replace the ordinary shift f h (x)=f(x+h) by an averaged shift determined by Steklov's function s h (f)(x)=1/h ∫ 0 h f(x+t)dt." @default.
• W208007606 created "2016-06-24" @default.
• W208007606 creator A5066843289 @default.
• W208007606 date "2013-09-23" @default.
• W208007606 modified "2023-09-23" @default.
• W208007606 title "On Direct And Inverse Theorems Of Approximation Theory In Variable Lebesgue And Sobolev Spaces" @default.
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