ISSN:
1618-1891
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary It is known[5] that if sm, n (x, y) are the partial sums of theFourier series of a funtion f(x, y) belonging to the class Lp, (p〉1), then $$\{ (m + 1)(n + 1)\} ^{ - 1} \mathop \Sigma \limits_{\mu = 0}^m \mathop \Sigma \limits_{v = 0}^n s_{\mu ,v} (x,y) \to f(x,y).(m,n) \to \infty ,$$ at almost every (x, y). FurtherHsü, Hai-Tsin (4) proved that, if f(x, y) belong to Lp and if k is any positive integer, then $$\{ (m + 1)(n + 1)\} ^{ - 1} \mathop \Sigma \limits_{\mu = 0}^m \mathop \Sigma \limits_{v = 0}^n |s_{\mu ,v} - f|^k \to 0asm,n \to \infty .$$ The object of this paper is to extend the result ofHsü by replacing sm, n by itsCesàro trasform of positive orders in general.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02411734
Permalink