Geodesic
Semi-norms and continuity modules of functions defined on a segment
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 155-203
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We describe in detail fundamental properties of continuity modules of various orders in the spaces $L^p$ of functions defined on a finite segment. We establish some general estimates of seminorms in terms of continuity modules with the best known constants. An example of application of these results to the best approximations is considered. 
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     author = {V. V. Zhuk and G. I. Natanson},
     title = {Semi-norms and continuity modules of functions defined on a~segment},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {155--203},
     year = {2001},
     volume = {276},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a7/}
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V. V. Zhuk; G. I. Natanson. Semi-norms and continuity modules of functions defined on a segment. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 155-203. http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a7/