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- W4383906326 abstract "This study gives a kind of sharp Wirtinger inequalities (Pizone inequalities) ∥f(k)∥p≤Bn,k,p,q(b−a)n−k+1/p−1/q∥f(n)∥qfor all 1≤p,q≤∞,0≤k≤n−1, where f∈Wqn[a,b] with at least n zeros (counting multiplicity) in [a,b]. First, based on the Hermite (Lagrange) interpolation, we express f as a Lagrange type (integral type) remainder. Second, we refer the computation of Bn,k,p,∞ to the maximum value problem of a multivariate function, and we give the values of Bn,k,p,∞ by finding the solution of the multivariate function aforementioned. At last, we refer the computation of Bn,k,p,q(1≤q<∞) to the norm of an integral operator. Our results are corrections and extensions to the results that appear in [J. C. Kuang, Applied Inequalities (Shandong Science and Technology Press, Jinan, 2004); A. Yu. Levin, Some estimates for a diff erentiable function, Dokl. Akad. Nauk SSSR 138 (1961) 37-38 (in Russian)]." @default.
- W4383906326 created "2023-07-12" @default.
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- W4383906326 date "2023-07-07" @default.
- W4383906326 modified "2023-09-25" @default.
- W4383906326 title "A kind of sharp Wirtinger inequalities" @default.
- W4383906326 doi "https://doi.org/10.1142/s0219691323500364" @default.
- W4383906326 hasPublicationYear "2023" @default.
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