A nonlinear partial differential equation and the unconditional constant of the Haar system in 𝐿^{𝑝}

Burkholder, D. L.

doi:10.1090/S0273-0979-1982-15061-3

A nonlinear partial differential equation and the unconditional constant of the Haar system in $L^p$

Author: D. L. Burkholder
Journal: Bull. Amer. Math. Soc. 7 (1982), 591-595
MSC (1980): Primary 46E30, 60G46; Secondary 35C05
DOI: https://doi.org/10.1090/S0273-0979-1982-15061-3
MathSciNet review: 670133
Full-text PDF Free Access

1. D. J. Aldous, Unconditional bases and martingales in 𝐿_{𝑝}(𝐹), Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 1, 117–123. MR 510406, https://doi.org/10.1017/S0305004100055559
2. D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494–1504. MR 208647, https://doi.org/10.1214/aoms/1177699141
3. D. L. Burkholder, A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional, Ann. Probab. 9 (1981), no. 6, 997–1011. MR 632972
4. D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), no. 3, 647–702. MR 744226
5. J. Lindenstrauss and A. Pełczyński, Contributions to the theory of the classical Banach spaces, J. Functional Analysis 8 (1971), 225–249. MR 0291772, https://doi.org/10.1016/0022-1236(71)90011-5
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: Espaces Lsup𝑝, applications radonifiantes et géométrie des espaces de Banach, Exp. Nos. I et II, Centre Math., École Polytech., Paris, 1975, pp. 26 pp. (erratum, p. 1) (French). MR 0420839
8. A. M. Olevskiĭ, Fourier series and Lebesgue functions, Uspehi Mat. Nauk 22 (1967), no. 3 (135), 237–239 (Russian). MR 0212485
9. A. M. Olevskiĭ, Fourier series with respect to general orthogonal systems, Springer-Verlag, New York-Heidelberg, 1975. Translated from the Russian by B. P. Marshall and H. J. Christoffers; Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 86. MR 0470599
10. R. E. A. C. Paley, A remarkable series of orthogonal functions. I, Proc. London Math. Soc. 34 (1932), 241-264.
11. Juljusz Schauder, Eine Eigenschaft des Haarschen Orthogonalsystems, Math. Z. 28 (1928), no. 1, 317–320 (German). MR 1544958, https://doi.org/10.1007/BF01181164