ACTA issues

## Classes of functions and Riemann means of Fourier series

F. Kádár, G. Rékai

Acta Sci. Math. (Szeged) 65:3-4(1999), 577-584
2704/2009

 Abstract. We consider the Riemann means of trigonometric series. Results proved: (i) A necessary and sufficient condition for a trigonometric series to be the Fourier series of a function in the periodic real Hardy space $H^1(T)$ is the boundedness of its Riemann means $S_h$ in $H^1$-norm. (ii) A necessary and sufficient condition for a trigonometric series to be the Fourier series of a function in the periodic ${\rm BMO}$ space is the boundedness of its Riemann means in the ${\rm BMO}$-norm. AMS Subject Classification (1991): 42A16, 42A24, 42A38 Received February 3, 1999, and in revised form March 9, 1999. (Registered under 2704/2009.)