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
References | Similar Articles | Additional Information
- D. J. Aldous, Unconditional bases and martingales in $L_{p}(F)$, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 1, 117–123. MR 510406, DOI https://doi.org/10.1017/S0305004100055559
- D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494–1504. MR 208647, DOI https://doi.org/10.1214/aoms/1177699141
- 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
- D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), no. 3, 647–702. MR 744226
- J. Lindenstrauss and A. Pełczyński, Contributions to the theory of the classical Banach spaces, J. Functional Analysis 8 (1971), 225–249. MR 0291772, DOI https://doi.org/10.1016/0022-1236%2871%2990011-5 6. J. Marcinkiewicz, Quelques théorèmes sur les séries orthogonales, Ann. Soc. Polon. Math. 16 (1937), 84-96.
- B. Maurey, Système de Haar, Séminaire Maurey-Schwartz 1974–1975: Espaces L$\sup {p}$, 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
- A. M. Olevskiĭ, Fourier series and Lebesgue functions, Uspehi Mat. Nauk 22 (1967), no. 3 (135), 237–239 (Russian). MR 0212485
- 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.
- Juljusz Schauder, Eine Eigenschaft des Haarschen Orthogonalsystems, Math. Z. 28 (1928), no. 1, 317–320 (German). MR 1544958, DOI https://doi.org/10.1007/BF01181164
Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 46E30, 60G46, 35C05
Retrieve articles in all journals with MSC (1980): 46E30, 60G46, 35C05