Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1994. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 22)

NAGY, K., Norm convergenc e of Fejér means of certain functions with respect to respect to UDMD product systems

Norm convergence of Fejér means of certain functions . . . 125 c

3_ie{o,i} i I,...,f

s_i6{0,l} £

s_l=£

ä_l=0 «•-Y wer )«'-ï w«-!

1 («MA w := := Z) fxe(x)xï(*)x7{t)Xi(t)dX(t). £,£G{0,1}

32X{0}/x / Xe)x?(a;

)x7(í)Xc

(í

A

) / 0 if £

k+i = £k+i,-,£

s-i = £

s-i- (see [3], r x hk [4]). From this fact and \<f>j(x)\ = 1 (

J

GN

,

Î

GÎÎ

) we get / |/CiK<)l

2rfA(i)< ii d\(t) < ±2

kr = r. J

hk £,

£'6{0,l}ä-2

x{0

} J

x ck + l

=

ik+l cs-l=

fs-l * Let P S}f and observe that "Ii - / = <£(/ -P) + (P-f) + tâP- P). Using the fact {S

lS

Jf){x) = (S

mi

n(i,j)f){

x) we ca

n show p = \ Ê<

5>/ s"/) = i=

1 From the inequality II/

<«*(/,2-) k*(/-i>)MI< / |/(t)-P(t)||ir;(x,i)|dA(i) <u

x(f,2~

s) [ \K*(x,t)\dX(t)<Su

x(f,2~

s), Jü that is we have and