Remarks on product $\text {VMO}$
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- by Michael T. Lacey, Erin Terwilleger and Brett D. Wick PDF
- Proc. Amer. Math. Soc. 134 (2006), 465-474 Request permission
Abstract:
Well known results related to the compactness of Hankel operators of one complex variable are extended to little Hankel operators of two complex variables. Critical to these considerations is the result of Ferguson and Lacey (2002) characterizing the boundedness of the little Hankel operators in terms of the product BMO of S.-Y. Chang and R. Fefferman (1985), (1980).References
- Gรฉrard Bourdaud, Remarques sur certains sous-espaces de $\textrm {BMO}(\Bbb R^n)$ et de $\textrm {bmo}(\Bbb R^n)$, Ann. Inst. Fourier (Grenoble) 52 (2002), no.ย 4, 1187โ1218 (French, with English and French summaries). MR 1927078
- Sun-Yung A. Chang and Robert Fefferman, Some recent developments in Fourier analysis and $H^p$-theory on product domains, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no.ย 1, 1โ43. MR 766959, DOI 10.1090/S0273-0979-1985-15291-7
- Sun-Yung A. Chang and Robert Fefferman, A continuous version of duality of $H^{1}$ with BMO on the bidisc, Ann. of Math. (2) 112 (1980), no.ย 1, 179โ201. MR 584078, DOI 10.2307/1971324
- R. R. Coifman, R. Rochberg, and Guido Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. (2) 103 (1976), no.ย 3, 611โ635. MR 412721, DOI 10.2307/1970954
- Sarah H. Ferguson and Michael T. Lacey, A characterization of product BMO by commutators, Acta Math. 189 (2002), no.ย 2, 143โ160. MR 1961195, DOI 10.1007/BF02392840
- Sarah H. Ferguson and Cora Sadosky, Characterizations of bounded mean oscillation on the polydisk in terms of Hankel operators and Carleson measures, J. Anal. Math. 81 (2000), 239โ267. MR 1785283, DOI 10.1007/BF02788991
- Zeev Nehari, On bounded bilinear forms, Ann. of Math. (2) 65 (1957), 153โ162. MR 82945, DOI 10.2307/1969670
- Vladimir V. Peller, Hankel operators and their applications, Springer Monographs in Mathematics, Springer-Verlag, New York, 2003. MR 1949210, DOI 10.1007/978-0-387-21681-2
- Donald Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391โ405. MR 377518, DOI 10.1090/S0002-9947-1975-0377518-3
Additional Information
- Michael T. Lacey
- Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
- MR Author ID: 109040
- Email: lacey@math.gatech.edu
- Erin Terwilleger
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269-3009
- Email: terwilleger@math.uconn.edu
- Brett D. Wick
- Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
- MR Author ID: 766171
- ORCID: 0000-0003-1890-0608
- Email: bwick@math.brown.edu
- Received by editor(s): May 7, 2004
- Received by editor(s) in revised form: September 21, 2004
- Published electronically: July 7, 2005
- Additional Notes: The first author was supported by an NSF grant.
The second authorโs research was supported in part by an NSF VIGRE grant to the Georgia Institute of Technology.
The third authorโs research was supported in part by an NSF VIGRE grant to Brown University. - Communicated by: Joseph A. Ball
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 465-474
- MSC (2000): Primary 42B30, 47B35
- DOI: https://doi.org/10.1090/S0002-9939-05-07974-8
- MathSciNet review: 2176015