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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.)
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