A lifting theorem and uniform algebras
HTML articles powered by AMS MathViewer
- by Takahiko Nakazi and Takanori Yamamoto PDF
- Trans. Amer. Math. Soc. 305 (1988), 79-94 Request permission
Abstract:
In this paper we discuss the possible generalizations of a lifting theorem of a $2 \times 2$ matrix to uniform algebras. These have applications to Hankel operators, weighted norm inequalities for conjugation operators and Toeplitz operators on uniform algebras. For example, the Helson-Szegö theorems for general uniform algebras follow.References
- Rodrigo Arocena and Mischa Cotlar, A generalized Herglotz-Bochner theorem and $L^{2}$-weighted inequalities with finite measures, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 258–269. MR 730071
- Rodrigo Arocena, Mischa Cotlar, and Cora Sadosky, Weighted inequalities in $L^{2}$ and lifting properties, Mathematical analysis and applications, Part A, Adv. in Math. Suppl. Stud., vol. 7, Academic Press, New York-London, 1981, pp. 95–128. MR 634237
- Klaus Barbey and Heinz König, Abstract analytic function theory and Hardy algebras, Lecture Notes in Mathematics, Vol. 593, Springer-Verlag, Berlin-New York, 1977. MR 0442690
- Mischa Cotlar and Cora Sadosky, On the Helson-Szegő theorem and a related class of modified Toeplitz kernels, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978) Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 383–407. MR 545279
- M. Cotlar and C. Sadosky, Lifting properties, Nehari theorem and Paley lacunary inequality, Rev. Mat. Iberoamericana 2 (1986), no. 1-2, 55–71. MR 864653, DOI 10.4171/RMI/25 T. Gamelin, Uniform algebras, 2nd ed., Chelsea, New York, 1984.
- John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
- Henry Helson and Gabor Szegö, A problem in prediction theory, Ann. Mat. Pura Appl. (4) 51 (1960), 107–138. MR 121608, DOI 10.1007/BF02410947
- I. I. Hirschman Jr. and Richard Rochberg, Conjugate function theory in weak$^{\ast }$ Dirichlet algebras, J. Functional Analysis 16 (1974), 359–371. MR 0380418, DOI 10.1016/0022-1236(74)90055-x
- Paul Koosis, Weighted quadratic means of Hilbert transforms, Duke Math. J. 38 (1971), 609–634. MR 288529
- Paul Koosis, Moyennes quadratiques pondérées de fonctions périodiques et de leurs conjuguées harmoniques, C. R. Acad. Sci. Paris Sér. A-B 291 (1980), no. 4, A255–A257 (French, with English summary). MR 591744
- Takahiko Nakazi, Norms of Hankel operators and uniform algebras, Trans. Amer. Math. Soc. 299 (1987), no. 2, 573–580. MR 869222, DOI 10.1090/S0002-9947-1987-0869222-8 —, Norms of Hankel operators and uniform algebras. II, Tôhoku Math. J. (to appear).
- Yoshiki Ohno, Remarks on Helson-Szegö problems, Tohoku Math. J. (2) 18 (1966), 54–59. MR 203519, DOI 10.2748/tmj/1178243480
- Takanori Yamamoto, On the generalization of the theorem of Helson and Szegő, Hokkaido Math. J. 14 (1985), no. 1, 1–11. MR 781822, DOI 10.14492/hokmj/1381757685
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 305 (1988), 79-94
- MSC: Primary 46J10; Secondary 47B35
- DOI: https://doi.org/10.1090/S0002-9947-1988-0920147-X
- MathSciNet review: 920147