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On a multidimensional form of F. Riesz's ``rising sun" lemma
Author(s):
A.
A.
Korenovskyy;
A.
K.
Lerner;
A.
M.
Stokolos
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1437-1440.
MSC (2000):
Primary 42B25
Posted:
November 22, 2004
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Abstract:
A multidimensional version of the Riesz rising sun lemma is proved by means of a generalized dyadic process.
References:
- 1.
- A.S. Besicovitch, On differentiation of Lebesgue double integrals, Fundam. Math. 25 (1935), 209-216.
- 2.
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- 3.
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- 4.
- M. de Guzmán, Differentiation of integrals in
 , Lecture Notes in Math., 481, Springer-Verlag 1975. MR 0457661 (56:15866) - 5.
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- 6.
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- 7.
- A.A. Korenovskii, The reverse Hölder inequality, the Muckenhoupt condition, and equimeasurable permutations of functions, Russian Acad. Sci. Dokl. Math. 45, no. 2 (1992), 301-304. MR 1191537 (93i:26014)
- 8.
- A.A. Korenovskii, Sharp extension of a reverse Hölder inequality and the Muckenhoupt condition, Math. Notes 52, no. 6 (1992), 1192-1201. MR 1208001 (94g:42031)
- 9.
- A.A. Korenovskyy, On the Gurov-Reshetnyak class of functions, submitted.
- 10.
- A.A. Korenovskyy, The Riesz rising sun lemma for several variables and John-Nirenberg inequality, Math. Notes, to appear.
- 11.
- F. Riesz, Sur l'existence de la dérivée des fonctions monotones et sur quelques problèmes qui s'y rattachent, Acta Sci. Math. Szeged 5 (1932), 208-221.
- 12.
- F. Riesz, Sur un théorème de maximum de MM. Hardy et Littlewood, J. London Math. Soc. 7(1932),
10-13. - 13.
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 , Amer. J. Math. 105(1983), 1231-1233. MR 0714775 (86a:28003) - 14.
- E.M. Stein, Singular integrals: the roles of Calderón and Zygmund, Notices Amer. Math. Soc. 45(1998), no. 9, 1130-1140. MR 1640159 (99f:42002)
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Additional Information:
A.
A.
Korenovskyy
Affiliation:
Department of Mathematical Analysis, IMEM, National University of Odessa, Dvoryanskaya, 2, 65026 Odessa, Ukraine
Email:
anakor@paco.net
A.
K.
Lerner
Affiliation:
Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel
Email:
aklerner@netvision.net.il
A.
M.
Stokolos
Affiliation:
Department of Mathematical Sciences, DePaul University, Chicago, Illinois, 60614
Email:
astokolo@depaul.edu
DOI:
10.1090/S0002-9939-04-07653-1
PII:
S 0002-9939(04)07653-1
Keywords:
``Rising sun" lemma,
dyadic property,
differential basis
Received by editor(s):
August 13, 2003
Received by editor(s) in revised form:
January 15, 2004
Posted:
November 22, 2004
Additional Notes:
The work of the first author was partially supported by the France-Ukraine program of scientific collaboration ``DNIPRO"
Communicated by:
Andreas Seeger
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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