Abstract. New Wiener amalgam spaces are introduced for local Hardy spaces. It is proved that the maximal Fejér operator is bounded from the amalgam space $W(h_{p},\ell_\infty )$ to $W(L_{p},\ell_\infty )$. This implies the almost everywhere convergence of the Fejér means for all $f\in W(L_{1},\ell_\infty )\supset L_1$.

AMS Subject Classification (1991): 42B08, 46E30; 42B30, 42A38

Keyword(s): Wiener amalgam spaces, local Hardy spaces, Fejér summability, Fourier transforms, atomic decomposition

Received October 10, 2008. (Registered under 6430/2009.)