Absztrakt: | The C($\alpha$,$\beta)$-means, which are the Cesaro means for
double series, of general double orthogonal series are estimated.
The author extends his earlier results on C(1,1)-means to the
parameter range $\alpha,\beta >0$ getting this way the order
$o\sb x(\log \log m\cdot \log \log n)$ a.e.. This is not too
surprising, however with his method he is able to derive another
estimate involving quadratic averages of C(0,0)- (and even C($\alpha$,0),
$\alpha >-1/2)$ means with respect to the first summing index
m which is remarkable, namely instead of the order $o\sb x(\log
m\cdot \log n)$ that one would expect he gets $o\sb x(\log \log
m\cdot \log n)$ a.e. for them.}
\RV{V.Totik |