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A nonlinear partial differential equation and the unconditional constant of the Haar system in $L^p$
Author(s):
D. L.
Burkholder
Journal:
Bull. Amer. Math. Soc.
7
(1982),
591-595.
MSC (1980):
Primary 46E30, 60G46;
Secondary 35C05
MathSciNet review:
670133
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References:
- 1.
- D. J. Aldous, Unconditional bases and martingales in L, Math. Proc. Cambridge Philos. Soc. 85 (1979), 117-123. MR 510406
- 2.
- D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494-1504. MR 208647
- 3.
- D. L. Burkholder, A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional, Ann. Probab. 9 (1981), 997-1011. MR 632972
- 4.
- D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann.Probab. (to appear). MR 744226
- 5.
- J. Lindenstrauss and A. Pelczyński, Contributions to the theory of the classical Banach spaces, J. Funct. Anal. 8 (1971), 225-249. MR 291772
- 6.
- J. Marcinkiewicz, Quelques théorèmes sur les séries orthogonales, Ann. Soc. Polon. Math. 16 (1937), 84-96.
- 7.
- B. Maurey, Système de Haar, Séminaire Maurey-Schwartz (1974-1975), École Polytechnique, Paris, 1975. MR 420839
- 8.
- A. M. Olevskiĭ, Fourier series and Lebesgue functions, Uspehi Mat. Nauk 22 (1967), 237-239. (Russian) MR 212485
- 9.
- A. M. Olevskiĭ, Fourier series with respect to general orthogonal systems, Springer-Verlag, New York-Heidelberg-Berlin, 1975. MR 470599
- 10.
- R. E. A. C. Paley, A remarkable series of orthogonal functions. I, Proc. London Math. Soc. 34 (1932), 241-264.
- 11.
- J. Schauder, Eine Eigenschaft des Haarschen Orthogonalsystems, Math. Z. 28 (1928), 317-320. MR 1544958
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Additional Information:
DOI:
10.1090/S0273-0979-1982-15061-3
PII:
S 0273-0979(1982)15061-3
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