Free interpolation in Hardy-Orlicz spaces

Andreas Hartmann

Studia Mathematica (1999)

  • Volume: 135, Issue: 2, page 179-190
  • ISSN: 0039-3223

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Hartmann, Andreas. "Free interpolation in Hardy-Orlicz spaces." Studia Mathematica 135.2 (1999): 179-190. <http://eudml.org/doc/216649>.

@article{Hartmann1999,
abstract = {},
author = {Hartmann, Andreas},
journal = {Studia Mathematica},
keywords = {free interpolation; Hardy-Orlicz spaces; interpolating sequences; Carleson condition; Hardy-Orlicz space},
language = {eng},
number = {2},
pages = {179-190},
title = {Free interpolation in Hardy-Orlicz spaces},
url = {http://eudml.org/doc/216649},
volume = {135},
year = {1999},
}

TY - JOUR
AU - Hartmann, Andreas
TI - Free interpolation in Hardy-Orlicz spaces
JO - Studia Mathematica
PY - 1999
VL - 135
IS - 2
SP - 179
EP - 190
AB -
LA - eng
KW - free interpolation; Hardy-Orlicz spaces; interpolating sequences; Carleson condition; Hardy-Orlicz space
UR - http://eudml.org/doc/216649
ER -

References

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  1. [1] L. Carleson, An interpolation problem for analytic functions, Amer. J. Math. 80 (1958), 921-930. Zbl0085.06504
  2. [2] D. L. Fernandez and J. B. Garcia, Interpolation of Orlicz-valued function spaces and U.M.D. property, Studia Math. 99 (1991), 23-40. Zbl0836.46067
  3. [3] J. B. Garnett, Bounded Analytic Functions, Academic Press, 1981. Zbl0469.30024
  4. [4] J. Gustavsson and J. Peetre, Interpolation of Orlicz spaces, Studia Math. 60 (1977), 33-59. Zbl0353.46019
  5. [5] A. Hartmann, Interpolation libre et caractérisation des traces de fonctions holomorphes sur les réunions finies de suites de Carleson, PhD thesis, Université Bordeaux I, 1996. 
  6. [6] A. Hartmann, Une approche de l’interpolation libre généralisée par la théorie des opérateurs et caractérisation des traces H p | Λ , J. Operator Theory 35 (1996), 281-316. 
  7. [7] A. Hartmann, Traces of certain classes of holomorphic functions on finite unions of Carleson sequences, Glasgow Math. J., to appear. Zbl1151.30346
  8. [8] M. Hasumi and S. Kataoka, Remarks on Hardy-Orlicz classes, Arch. Math. (Basel) 51 (1988), 455-463. Zbl0657.30026
  9. [9] P. Jones, L -estimates for the ¯ -problem in a half plane, Acta Math. 150 (1983), 137-152. Zbl0516.35060
  10. [10] V. Kabaĭla, Interpolation sequences for the H p classes in the case p < 1, Litovsk. Mat. Sb. 3 (1963), 141-147. 
  11. [11] M. A. Krasnosel'skii and Ya. Rutickii, Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961. 
  12. [12] R. Lesniewicz, On linear functionals in Hardy-Orlicz spaces, I, Studia Math. 46 (1973), 53-77. Zbl0294.46019
  13. [13] N. K. Nikol'skiĭ, Bases of invariant subspaces and operator interpolation, Proc. Steklov Inst. Math. 130 (1979), no. 4, 55-132. 
  14. [14] N. K. Nikol'skiĭ, Treatise on the Shift Operator, Springer, Berlin, 1986. 
  15. [15] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Pure and Appl. Math., Dekker, New York, 1991. Zbl0724.46032
  16. [16] M. Rosenblum and J. Rovnyak, Hardy Classes and Operator Theory, Oxford Univ. Press, New York, 1985. Zbl0586.47020
  17. [17] W. Rudin, Functional Analysis, McGraw-Hill, New York, 1973. 
  18. [18] R. Ryan, Conjugate functions in Orlicz spaces, Pacific J. Math. 13 (1963), 1371-1377. Zbl0133.37301
  19. [19] H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions, Amer. J. Math. 83 (1961), 513-532. Zbl0112.29701
  20. [20] V. I. Vasyunin, Unconditionally convergent spectral decompositions and interpolation problems, Proc. Steklov Inst. Math. 130 (1979), no. 4, 1-53. Zbl0438.47039
  21. [21] V. I. Vasyunin, Traces of bounded analytic functions on finite unions of Carleson sets, J. Soviet Math. 27 (1984), no. 1, 2448-2450. Zbl0543.30024
  22. [22] S. A. Vinogradov and V. P. Khavin, Free interpolation in H and some other classes of functions I, ibid. 9 (1978), no. 2, 137-171. Zbl0398.41002
  23. [23] S. A. Vinogradov and V. P. Khavin, Free interpolation in H and some other classes of functions II, ibid. 14 (1980), no. 2, 1027-1065. Zbl0442.41003

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