Pacific Journal of Mathematics

On the Hardy space $H^1$ on products of half-spaces.

Nativi Viana Pereira Bertolo

Article information

Pacific J. Math., Volume 138, Number 2 (1989), 347-356.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46E15: Banach spaces of continuous, differentiable or analytic functions
Secondary: 32A35: Hp-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15] 42B30: $H^p$-spaces


Bertolo, Nativi Viana Pereira. On the Hardy space $H^1$ on products of half-spaces. Pacific J. Math. 138 (1989), no. 2, 347--356.

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  • [3] The equivalence of H^b(R x R) and^ xR%). 3.1. THEOREM, (i) 7/"F = (uk;k e D) belongs to H*ne(Rl x R^.), ere exists an f e L(R2)such that Hkf e L^R2) and uk = (PsPt) * Hkf for each k e D. Moreover, there is a positive constant C, indepen- dent ofF, such that (1) ken
  • [10] The equivalence of H^b(R x R) and^ xR%). 3.1. THEOREM, and of the maximal functions u*(G)(x9y) =su5 />0G(x9s\y9 ), we have / / sap\F(x9s;y9t)\dxdy J J 5,/>0 <CMo(Mo(u*(G))(x,y)dxdy < C\\u*(Gp < C\\g\p < C\\F\\HL. Hence, we have sup \F{x,s\y,t)\dxdy < C\\F\\W
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