Pacific Journal of Mathematics

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

Nativi Viana Pereira Bertolo

Article information

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

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102650154

Mathematical Reviews number (MathSciNet)
MR996205

Zentralblatt MATH identifier
0633.30030

Subjects
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

Citation

Bertolo, Nativi Viana Pereira. On the Hardy space $H^1$ on products of half-spaces. Pacific J. Math. 138 (1989), no. 2, 347--356. https://projecteuclid.org/euclid.pjm/1102650154


Export citation

References

  • [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
  • [I] N. V. P. Bertolo, Sobre desigualdades de subsharmonicidade e bisubhar- monicidade desistemas conjugados de Cauchy-Riemann generalizados,Anais Acad. Bras. Ci.,55 (1983),320-321.
  • [2] N. V. P. Bertolo, On the Hardy space H in product of half spaces, 20 Seminario Brasileiro de Analise, (1984),283-296.
  • [3] B. Bordin and D. L. Fernandez, Sobre os espaos Hp em productos desemi- espaos, Anais Acad. Bras. Ci., 55 (1983),319-320.
  • [4] S. Y. A. Chang and R. Fefferman, Some recent developments in Fourier Analysis and Hp theory on product domains, Bull. Amer. Math. Soc, 12 (1985), 1-43.
  • [5] R. R. Coifman and G. Weiss, On sub-harmonicity inequalities involvingso- lutions of generalized Cauchy-Riemann equations, Studia Mathematica, 36 (1970), 77-83.
  • [6] C. Fefferman and E. M. Stein, Hp spaces of several variables, Acta Math., 129(1972), 137-193.
  • [7] K. G. Merryfield, Hp Spaces in poly-half Spaces, Ph. D. dissertation, Uni- versity of Chicago, (1980).
  • [8] H. Sato, La classe de Hardy Hx defonctions biharmoniques sur Rm+1 x Rn+ sa caracterisation por les transformations de Riesz, C.R. Acad. Sc. Paris, t 291 (15 septembre1980).
  • [9] S. Sato, Lusin functions and nontangential maximal functions in the Hp theory on the product of upper half spaces, Thoku Math. J., 37 (1985), 1-13.
  • [10] E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton (1971).
  • [II] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press,1971.