# Young criterion

From Encyclopedia of Mathematics

One of the sufficiency criteria for the convergence of a Fourier series at a point. Let a function have period , be Lebesgue integrable over the interval and, on putting , let it satisfy at the point the conditions: 1) as ; 2) the function is of finite variation on the interval , , where is some fixed number; and 3) as . Then the Fourier series of at converges to (cf. [2]). Young's criterion is stronger than the Jordan criterion. It was established by W.H. Young [1].

#### References

[1] | W.H. Young, "On the convergence of the derived series of Fourier series" Proc. London Math. Soc. , 17 (1916) pp. 195–236 |

[2] | N.K. [N.K. Bari] Bary, "A treatise on trigonometric series" , Pergamon (1964) (Translated from Russian) |

#### Comments

#### References

[a1] | A. Zygmund, "Trigonometric series" , 2 , Cambridge Univ. Press (1988) |

**How to Cite This Entry:**

Young criterion.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Young_criterion&oldid=19222

This article was adapted from an original article by B.I. Golubov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article