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
126 Károly Nagy K/ - /II < lk*(/ - P)|| + Il P - /II + bip - P\\ <9u> x(f,2-) + \WlP-P\\. Since i I\al P-PII = ||S* (at / - /II < ||4 / - /II IWn f ~ f\\ ca n estimated by A(Ő). For 0 < a < | we have A(s) = 0 (2~ s a + 2"t2 s (^a )) = 0(2~ s a) = 0(n~ a) as n -> oo For a > y we have A (s) = 2-î a+2sJ22 k (*~ a ) = 0 (nQ + = 0 (^Jj asn-^oo. For a = \ we have as n ^ oo. This complétés the proof of the theorem. I would Hke to thank Professor G. Gát for setting the prob lem and his help. References [1] F., SCHIPP, W. R. WADE , P. SIMON and J. PÁL, Walsh Sériés. An Introduction to dyadic Harmonie Analysis, Akadémiai Kiadó, Budapest, and Adam Hilger, Bristol and New York (1990). [2] G. GÁT, Orthonormal System on Vilenkin Groups, Acta Math. Hungar. 58 (1-2) (1991), 193-198. [3] F., SCHIPP and W. R. WADE, Norm Convergence and Summability of Fourier Sériés with Respect to Certain Product System, (To appear.) [4] G. GÁT, Vilenkin-Firoer Sériés and Limit Periodic Arithmetic Functions, Colleguai mathematica societatis János Bolyai 58 (1990), 315332.
