Geodesic
Approximation via Hausdorff operators
Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 512-529

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DOI

Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate functions and the adjoint to that Hausdorff operator of the given function. We find estimates for the rate of approximation in various metrics in terms of the parameter of truncation and the components of the Hausdorff operator. Explicit rates of approximation of functions and comparison with approximate identities are given in the case of continuous functions from the class $\text {Lip }\alpha $.
DOI : 10.4153/S0008439520000612
Mots-clés : Hausdorff operators, approximation in Lebesgue spaces, moduli of continuity 
Debernardi, Alberto; Liflyand, Elijah. Approximation via Hausdorff operators. Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 512-529. doi: 10.4153/S0008439520000612
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     title = {Approximation via {Hausdorff} operators},
     journal = {Canadian mathematical bulletin},
     pages = {512--529},
     year = {2021},
     volume = {64},
     number = {3},
     doi = {10.4153/S0008439520000612},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000612/}
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