Annals of Functional Analysis

A note on weak-convergence in h1(Rd)

Ha Duy Hung, Duong Quoc Huy, and Luong Dang Ky

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We give a very simple proof of a result by Dafni that states that the weak-convergence is true in the local Hardy space h1(Rd).

Article information

Source
Ann. Funct. Anal., Volume 7, Number 4 (2016), 573-577.

Dates
Received: 21 January 2016
Accepted: 8 April 2016
First available in Project Euclid: 31 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.afa/1472659943

Digital Object Identifier
doi:10.1215/20088752-3661494

Mathematical Reviews number (MathSciNet)
MR3543149

Zentralblatt MATH identifier
1346.42022

Subjects
Primary: 42B30: $H^p$-spaces
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions

Keywords
$H^{1}$ BMO VMO Banach–Alaoglu

Citation

Hung, Ha Duy; Huy, Duong Quoc; Ky, Luong Dang. A note on weak $^{*}$ -convergence in $h^{1}(\mathbb{R}^{d})$. Ann. Funct. Anal. 7 (2016), no. 4, 573--577. doi:10.1215/20088752-3661494. https://projecteuclid.org/euclid.afa/1472659943


Export citation

References

  • [1] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645.
  • [2] G. Dafni, Local VMO and weak convergence in $h^{1}$, Canad. Math. Bull. 45 (2002), no. 1, 46–59.
  • [3] C. Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), no. 4, 587–588.
  • [4] D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), no. 1, 27–42.
  • [5] P. W. Jones and J.-L. Journé, On weak convergence in $H^{1}(\mathbf{R}^{d})$, Proc. Amer. Math. Soc. 120 (1994), no. 1, 137–138.
  • [6] L. D. Ky, Bilinear decompositions and commutators of singular integral operators, Trans. Amer. Math. Soc. 365 (2013), no. 6, 2931–2958.
  • [7] L. D. Ky, Endpoint estimates for commutators of singular integrals related to Schrödinger operators, Rev. Mat. Iberoam. 31 (2015), no. 4, 1333–1373.
  • [8] H. L. Royden, Real Analysis, 3rd ed., Macmillan, New York, 1988.