Differentiation theorem for Gaussian measures on Hilbert space
Author:
Jaroslav Tišer
Journal:
Trans. Amer. Math. Soc. 308 (1988), 655-666
MSC:
Primary 28C20; Secondary 28A15, 46G12
DOI:
https://doi.org/10.1090/S0002-9947-1988-0951621-8
MathSciNet review:
951621
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: It is shown that the differentiation theorem is valid in infinitely dimensional Hilbert space with certain Gaussian measures. The proof uses result from harmonic analysis concerning the behavior of Hardy-Littlewood maximal operator in highly dimensional space.
- [1] D. Preiss, Gaussian measures and covering theorems, Comment. Math. Univ. Carolin. 20 (1979), 95-99. MR 526149 (80e:28020)
- [2] -, Gaussian measures and the density theorem, Comment. Math. Univ. Carolin. 22 (1981), 181-193. MR 609946 (83d:28008)
- [3] -, Differentiation of measures in infinitely dimensional spaces, Proc. Topology and Measure III (Greifswald, 1982), Wissen. Beiträge d. Greifswald Univ., 1983, pp. 201-207. MR 677136 (85a:60015)
- [4] D. Preiss and J. Tišer, Differentiation of Gaussian measures on Hilbert space, Lecture Notes Math., vol. 945, Springer-Verlag, Berlin and New York, 1981, pp. 194-207.
- [5]
E. M. Stein and J. O. Strömberg, Behavior of maximal functions in
for large
, Ark. Mat. 21 (1983), 259-269. MR 727348 (86a:42027)
Retrieve articles in Transactions of the American Mathematical Society with MSC: 28C20, 28A15, 46G12
Retrieve articles in all journals with MSC: 28C20, 28A15, 46G12
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1988-0951621-8
Keywords:
Derivation,
Gaussian measure,
maximal operator
Article copyright:
© Copyright 1988
American Mathematical Society