×

Seminorms and continuity modules for functions defined on a segment. (English. Russian original) Zbl 1071.41008

J. Math. Sci., New York 118, No. 1, 4822-4851 (2003); translation from Zap. Nauchn. Semin. POMI 276, 155-203 (2001).
Summary: 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.

MSC:

41A10 Approximation by polynomials
30E10 Approximation in the complex plane
Full Text: DOI