Free interpolation in Hardy-Orlicz spaces

• Autorzy: Andreas Hartmann
• Języki publikacji: EN

Abstrakty

EN

We show that the Carleson condition is necessary and sufficient for free interpolation in Hardy-Orlicz spaces $ℋ_φ$ on the unit disk ⅅ under certain conditions on φ, and we give a characterization of the trace space $ℋ_φ|_Λ}$ if Λ is a finite union of Carleson sequences.

Słowa kluczowe

EN

free interpolation   Hardy-Orlicz spaces   interpolating sequences   Carleson condition  

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 30E05: Moment problems, interpolation problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 135
• Numer: 2
• Strony: 179-190

Daty

wydano

1999

otrzymano

1998-12-28

poprawiono

1999-02-23

Twórcy

autor

Andreas Hartmann

• UFR Mathématiques/Informatique, Université Bordeaux I, 351, cours de la Libération, 33405 Talence Cedex, France ,

Bibliografia

• [1] L. Carleson, An interpolation problem for analytic functions, Amer. J. Math. 80 (1958), 921-930.
• [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.
• [3] J. B. Garnett, Bounded Analytic Functions, Academic Press, 1981.
• [4] J. Gustavsson and J. Peetre, Interpolation of Orlicz spaces, Studia Math. 60 (1977), 33-59.
• [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] 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] A. Hartmann, Traces of certain classes of holomorphic functions on finite unions of Carleson sequences, Glasgow Math. J., to appear.
• [8] M. Hasumi and S. Kataoka, Remarks on Hardy-Orlicz classes, Arch. Math. (Basel) 51 (1988), 455-463.
• [9] P. Jones, $L^∞$-estimates for the $\overline ∂$-problem in a half plane, Acta Math. 150 (1983), 137-152.
• [10] V. Kabaĭla, Interpolation sequences for the $H_p$ classes in the case p < 1, Litovsk. Mat. Sb. 3 (1963), 141-147.
• [11] M. A. Krasnosel'skii and Ya. Rutickii, Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961.
• [12] R. Lesniewicz, On linear functionals in Hardy-Orlicz spaces, I, Studia Math. 46 (1973), 53-77.
• [13] N. K. Nikol'skiĭ, Bases of invariant subspaces and operator interpolation, Proc. Steklov Inst. Math. 130 (1979), no. 4, 55-132.
• [14] N. K. Nikol'skiĭ, Treatise on the Shift Operator, Springer, Berlin, 1986.
• [15] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Pure and Appl. Math., Dekker, New York, 1991.
• [16] M. Rosenblum and J. Rovnyak, Hardy Classes and Operator Theory, Oxford Univ. Press, New York, 1985.
• [17] W. Rudin, Functional Analysis, McGraw-Hill, New York, 1973.
• [18] R. Ryan, Conjugate functions in Orlicz spaces, Pacific J. Math. 13 (1963), 1371-1377.
• [19] H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions, Amer. J. Math. 83 (1961), 513-532.
• [20] V. I. Vasyunin, Unconditionally convergent spectral decompositions and interpolation problems, Proc. Steklov Inst. Math. 130 (1979), no. 4, 1-53.
• [21] V. I. Vasyunin, Traces of bounded analytic functions on finite unions of Carleson sets, J. Soviet Math. 27 (1984), no. 1, 2448-2450.
• [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.
• [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.