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
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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), no. 1, 95–99. MR 526149
- [2] D. Preiss, Gaussian measures and the density theorem, Comment. Math. Univ. Carolin. 22 (1981), no. 1, 181–193. MR 609946
- [3] David Preiss, Differentiation of measures in infinitely-dimensional spaces, Proceedings of the Conference Topology and Measure III, Part 1, 2 (Vitte/Hiddensee, 1980) Wissensch. Beitr., Ernst-Moritz-Arndt Univ., Greifswald, 1982, pp. 201–207. MR 677136
- [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 𝑅ⁿ for large 𝑛, Ark. Mat. 21 (1983), no. 2, 259–269. MR 727348, https://doi.org/10.1007/BF02384314
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, Ark. Mat. 21 (1983), 259-269. Retrieve articles in Transactions of the American Mathematical Society with MSC: 28C20, 28A15, 46G12
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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
