Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Holomorphic martingales and interpolation between Hardy spaces: the complex method

Author: P. F. X. Müller
Journal: Trans. Amer. Math. Soc. 347 (1995), 1787-1792
MSC: Primary 60G46; Secondary 42B30, 46E15, 46M35
MathSciNet review: 1264825
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A probabilistic proof is given to identify the complex interpolation space of ${H^1}(\mathbb {T})$ and ${H^\infty }(\mathbb {T})$ as ${H^p}(\mathbb {T})$.

References [Enhancements On Off] (What's this?)

    J. Berg and J. Löfström, Interpolation spaces, Springer Verlag, New York, 1976.
  • J. Bourgain, New Banach space properties of the disc algebra and $H^{\infty }$, Acta Math. 152 (1984), no. 1-2, 1–48. MR 736210, DOI
  • ---, Some consequences of Pisier’s approach to interpolations, preprint 1991.
  • Richard Durrett, Brownian motion and martingales in analysis, Wadsworth Mathematics Series, Wadsworth International Group, Belmont, CA, 1984. MR 750829
  • Peter W. Jones, $L^{\infty }$ estimates for the $\bar \partial $ problem in a half-plane, Acta Math. 150 (1983), no. 1-2, 137–152. MR 697611, DOI
  • Svante Janson and Peter W. Jones, Interpolation between $H^{p}$ spaces: the complex method, J. Functional Analysis 48 (1982), no. 1, 58–80. MR 671315, DOI
  • S. V. Kislyakov, Truncating functions in weighted ${H^p}$ and two theorems of J. Bourgain, Uppsala University, Dept. of Math., Report 1989:10.
  • S. V. Kislyakov, Absolutely summing operators on the disc algebra, Algebra i Analiz 3 (1991), no. 4, 1–77 (Russian); English transl., St. Petersburg Math. J. 3 (1992), no. 4, 705–774. MR 1152601
  • S. V. Kislyakov and Q, Xu, Interpolation of weighted and vector valued Hardy spaces, Publ. Inst. Recherche. Math. Lille 25 (1991).
  • Paul F. X. Müller, Holomorphic martingales and interpolation between Hardy spaces, J. Anal. Math. 61 (1993), 327–337. MR 1253447, DOI
  • Gilles Pisier, Interpolation between $H^p$ spaces and noncommutative generalizations. I, Pacific J. Math. 155 (1992), no. 2, 341–368. MR 1178030
  • Nicholas Th. Varopoulos, The Helson-Szegő theorem and $A_{p}$-functions for Brownian motion and several variables, J. Functional Analysis 39 (1980), no. 1, 85–121. MR 593791, DOI
  • Q. Xu, Elementary proofs of two theorems of P.W. Jones on interpolation between Hardy spaces, Ann. Inst. Fourier (Grenoble) 42 (1992), 875-889. ---, Notes on interpolation of Hardy spaces, preprint 1990.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60G46, 42B30, 46E15, 46M35

Retrieve articles in all journals with MSC: 60G46, 42B30, 46E15, 46M35

Additional Information

Keywords: Holomorphic martingales, complex interpolation method, Hardy spaces
Article copyright: © Copyright 1995 American Mathematical Society