, Volume 42, Issue 2, pp 174-182

Marcinkiewicz integral on hardy spaces

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In this paper we prove that the Marcinkiewicz integral μΩ is an operator of type (H 1,L 1) and of type (H 1,∞,L 1,∞). As a corollary of the results above, we obtain again the the weak type (1,1) boundedness of μΩ, but the smoothness condition assumed on Ω is weaker than Stein's condition.