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

GÁT, G., On a norm convergence theorem with respect to the Vilenkin system in the Hardy spaces

106 György Gát This follows Mfc+i-l .. „ Mfc+i-1 1 \\bnfk\\

i > C log n

k "ilt-1 1 1 2 c v- log n

k log m

k logMjt+i , n

k \ogM

k+

1 ' n

k= 1 Define the sequences of indices i £ P such that log

2 m ^fc - > e (k e p). log M^ + Set The

n H/ll^ < E,~i MIAJI^ < c. log M, n=M

V

k 6 n=M„

f

c V 7 M^+i-1 fc-1 ra^ Jk ii^g^xK/1 > ck log M, for all A; G P. That is E [EjîWM |i /» = <*-c, 1 " sup V \\S

kf\\i/k = oo. n log n^ References [1] AGAEV, G. H., VlLENKIN, N. Ja., DZHAFARLI, G. M., RUBINSTEIN, A. I., Multiplicative systems of fonctions and harmonie analysis on 0-dimension al groups, Izd. ("ELM"), Baku, (1981). (in Russian). [2] FRIDLI S., SIMON, P., On the Dirichlet kernels and a Hardy space with respect to the Vilenkin system, Acta Math. Hung., 45 (1-2) (1985), 223-234.