ACTA issues

Paley type inequalities and multipliers for Ciesielski-Fourier series

Ferenc Weisz

Acta Sci. Math. (Szeged) 70:1-2(2004), 77-89

Abstract. The well-known Paley type inequality $$\Big(\sum_{i=0}^\infty2^{i(2-2/p)} |{\hat f}(2^i)|^2 \Big)^{1/2} \leq C_p\|f\|_{H^p}\qquad(0< p\leq1)$$ is generalized for one- and more-parameter Ciesielski--Fourier coefficients and for Hardy spaces.

AMS Subject Classification (1991): 41A15, 42B05, 42C10, 42B30

Keyword(s): Paley type inequalities, multipliers, Walsh system, spline functions, Ciesielski system, Hardy spaces, atomic decomposition

Received September 5, 2003. (Registered under 5800/2009.)