Geodesic
Sharp Estimates of Integrals in Terms of the Second Modulus of Continuity
Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 483-495

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For a certain class of kernels, the exact constant in the estimate of the integral of the product of two functions in terms of the second modulus of continuity of one of them is obtained. Estimates of best approximations by entire functions of exponential type and by splines in terms of the second modulus of continuity of the second derivative of the approximated function are derived from the results obtained. The constants in these estimates are smaller than the previously known ones.
Keywords: estimate of the integral of the product of two functions, best approximation by entire functions, best approximation by splines, second modulus of continuity, Jackson-type inequality. 
@article{MZM_2014_96_4_a0,
     author = {O. L. Vinogradov},
     title = {Sharp {Estimates} of {Integrals} in {Terms} of the {Second} {Modulus} of {Continuity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--495},
     publisher = {mathdoc},
     volume = {96},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a0/}
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O. L. Vinogradov. Sharp Estimates of Integrals in Terms of the Second Modulus of Continuity. Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 483-495. http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a0/