An integral inequality for the disc multiplier
Author:
A. Córdoba
Journal:
Proc. Amer. Math. Soc. 92 (1984), 407408
MSC:
Primary 42B15; Secondary 35S05
MathSciNet review:
759664
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Abstract: In this paper an integral inequality is proved for the BochnerRiesz operators in dimension two. This inequality expresses how those operators are controlled by maximal functions associated to families of rectangles with an appropriate number of directions.
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 A. Córdoba, The Kakeya maximal function and the spherical summation multipliers, Amer. J. Math. 99 (1977). MR 0447949 (56:6259)
 [2]
 , A note on BochnerRiesz operators, Duke Math. J. 46 (1979). MR 544242 (80m:42025)
 [3]
 , The multiplier problem for the polygon, Ann. of Math. (2) 105 (1977). MR 0438022 (55:10943)
 [4]
 A. Cordoba and B. LopezMelero, Spherical summation: a problem of E. M. Stein, Ann. Inst. Fourier (Grenoble) 31 (1981), fasc. 3. MR 638621 (83g:42008)
 [5]
 J. Rubio de Francia, Weighted norm inequalities and vector valued inequalities, Lecture Notes in Math., vol. 908, SpringerVerlag, Berlin and New York, 1982. MR 654181 (83h:42025)
 [6]
 E. M. Stein, Some problems in harmonic analysis, Proc. Sympos. Pure Math., Vol. 35, Part 1, Amer. Math. Soc., Providence, R. I., 1978, pp. 320. MR 545235 (80m:42027)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198407596646
PII:
S 00029939(1984)07596646
Article copyright:
© Copyright 1984
American Mathematical Society
