Characterizations of bounded mean oscillation on the polydisk in terms of Hankel operators and Carleson measures

Journal d'Analyse Mathematique

Volumn 81, Issue , 2000, Pages 239-267

  Ferguson, Sarah H ^a   Sadosky, Cora ^b  

^a WAYNE STATE UNIVERSITY   (United States)

^b HOWARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000051317     PISSN: 00217670     EISSN: 15658538     Source Type: Journal    
DOI: 10.1007/BF02788991     Document Type: Article

References (29)

1. [Aron] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337-404.
2. [Arv] W. Arveson, Interpolation problems in nest algebras, J. Funct. Anal. 20 (1975), 208-233.
3. [BaTi] M. Bakonyi and D. Timotin, On a conjecture of Cotlar and Sadosky on multidimensional Hankel operators, C.R. Acad. Sci. Paris, Series I 325, No. 10 (1997), 1071-1075.
4. [Bo] A. Bonami, Some comments on factorization in the bidisc, personal communication.
5. [Bon] F. F. Bonsall, Boundedness of Hankel Matrices, J. London Math. Soc. (2) 29 (1984), 289-300.
6. [Car] L. Carleson, Interpolation by bounded functions and the corona problem, Ann. of Math. (2) 76 (1962), 547-559.
7. p for the bi-disc, Mittag Leffler Report No. 7, 1974.
8. [Ch] S.-Y. A. Chang, Carleson measure on the bi-disc, Ann. of Math. (2) 109 (1979), 613-620.
9. 1 with BMO on the bi-disc, Ann. of Math. (2) 112 (1980), 179-201.
10. p theory on product domains, Bull. Amer. Math. Soc. 12 (1985), 1-43.
11. p of the bidimensional torus, in Harmonic Analysis and Partial Differential Equations (Boca Raton, FL 1988) (M. Milman and T. Schonbek, eds.), Contemporary Mathematics 107, Amer. Math. Soc., Providence, RI, 1990.
12. [CoSa1] M. Cotlar and C. Sadosky, Nehari and Nevalinna-Pick problems and holomorphic extensions in the polydisk in terms of restricted BMO, J. Funct. Anal. 121 (1994), 205-210.
13. [CoSa2] M. Cotlar and C. Sadosky, Two distinguished subspaces of product BMO and Nehari-AAK theory for Hankel operators on the torus, Integral Equations and Operator Theory 26 (1996), 273-304.
14. [CRW] R Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. (2) 103 (1976), 611-635.
15. p spaces of several variables, Acta Math. 129 (1972), 137-193.
16. [Fe] C. Fefferman, Characterization of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587-588.
17. [Fef] R. Fefferman, Bounded mean oscillation on the polydisc, Ann. of Math. (2) 110 (1979), 395-406.
18. [Fef1] R. Fefferman, Harmonic analysis on product spaces, Ann. of Math. (2) 126 (1987), 109-130.
19. [F] S. H. Ferguson, The Nehari Problem for the Hardy space of the torus, J. Operator Theory 40 (1998), 309-321.
20. [GR] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, Notas de Matemática (L. Nachbin, ed.), 116, North-Holland, Amsterdam, 1985.
21. [Gar] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
22. [JoNi] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426.
23. 1 and applications to the corona problem, Indiana Univ. Math. J. 45 (1996), 83-102.
24. [Lin] Ing-Jer Lin, Factorization theorems for Hardy spaces of the bidisc, 0 < p ≤ 1, Proc. Amer. Math. Soc. 124 (1996), 549-560.
25. [Ne] Z. Nehari, On bounded bilinear forms, Ann. of Math. (2) 65 (1957), 153-162.
26. [Nik] N. Nikol'skiǐ, Treatise on the Shift Operator, Springer-Verlag, Berlin, 1986.
27. [Pa] L. Page, Bounded and compact vectorial Hankel operators, Trans. Amer. Math. Soc. 150 (1970), 341-372.
28. [Sal] N. Salinas, Products of kernel functions and module tensor products, Oper. Theory Adv. Appl. 32 (1988), 219-241.
29. [Sar] D. E. Sarason, Function Theory on the Unit Circle, Notes for lectures given at Virginia Polytechnic Institute, Blacksburg, Virginia, 1978.