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A covering lemma for product spaces
Author:
Jean-Lin Journé
Journal:
Proc. Amer. Math. Soc. 96 (1986), 593-598
MSC:
Primary 42B20
MathSciNet review:
826486
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Abstract: We give a substitute for the Whitney decomposition of an arbitrary open set in  where squares are replaced by rectangles. Then we deduce the  -BMO boundedness of certain singular integral operators defined on product spaces.
- [1]
Sun-Yung
A. Chang, Carleson measure on the bi-disc, Ann. of Math. (2)
109 (1979), no. 3, 613–620. MR 534766
(80j:32009), http://dx.doi.org/10.2307/1971229
- [2]
Sun-Yung
A. Chang and Robert
Fefferman, A continuous version of duality of 𝐻¹ with
BMO on the bidisc, Ann. of Math. (2) 112 (1980),
no. 1, 179–201. MR 584078
(82a:32009), http://dx.doi.org/10.2307/1971324
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Ronald
R. Coifman and Yves
Meyer, Au delà des opérateurs
pseudo-différentiels, Astérisque, vol. 57,
Société Mathématique de France, Paris, 1978 (French).
With an English summary. MR 518170
(81b:47061)
- [4]
Robert
Fefferman and Elias
M. Stein, Singular integrals on product spaces, Adv. in Math.
45 (1982), no. 2, 117–143. MR 664621
(84d:42023), http://dx.doi.org/10.1016/S0001-8708(82)80001-7
- [5]
J.-L. Journé, Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón, Lecture Notes in Math., vol. 994, Springer-Verlag, Berlin and New York, 1983.
- [6]
-, Calderón-Zygmund operators on product spaces, Revista Ibero-Americana 3 (1985).
- [1]
- S.-Y. A. Chang, Carleson measure on the bi-disc, Ann. of Math. (2) 109 (1979), 613-620. MR 534766 (80j:32009)
- [2]
- S.-Y. A. Chang and R. Fefferman, A continuous version of duality of
 with BMO on the bi-disc, Ann. of Math. (2) 112 (1980), 179-201. MR 584078 (82a:32009)
- [3]
- R. R. Coifman and Y. Meyer, Au delà des opérateurs pseudo-differentiels, Astérisque No. 57, 1978. MR 518170 (81b:47061)
- [4]
- R. Fefferman and E. M. Stein, Singular integrals on product spaces, Adv. in Math. 45 (1982), 117-143. MR 664621 (84d:42023)
- [5]
- J.-L. Journé, Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón, Lecture Notes in Math., vol. 994, Springer-Verlag, Berlin and New York, 1983.
- [6]
- -, Calderón-Zygmund operators on product spaces, Revista Ibero-Americana 3 (1985).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1986-0826486-9
PII:
S 0002-9939(1986)0826486-9
Keywords:
Carleson measures,
Whitney decompostion
Article copyright:
© Copyright 1986 American Mathematical Society
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