Estimates for the maximal operator of the Ornstein-Uhlenbeck semigroup
HTML articles powered by AMS MathViewer
- by Cristian E. Gutiérrez and Wilfredo O. Urbina PDF
- Proc. Amer. Math. Soc. 113 (1991), 99-104 Request permission
Abstract:
We show pointwise estimates for the maximal operator of the Ornstein-Uhlenbeck semigroup for functions that are integrable with respect to the Gaussian measure. The estimates are used to prove pointwise convergence.References
- Calixto P. Calderón, Some remarks on the multiple Weierstrass transform and Abel summability of multiple Fourier-Hermite series, Studia Math. 32 (1969), 119–148. MR 262770, DOI 10.4064/sm-32-2-119-148
- Einar Hille, A class of reciprocal functions, Ann. of Math. (2) 27 (1926), no. 4, 427–464. MR 1502747, DOI 10.2307/1967695
- Benjamin Muckenhoupt, Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139 (1969), 231–242. MR 249917, DOI 10.1090/S0002-9947-1969-0249917-9
- Edward Nelson, Dynamical theories of Brownian motion, Princeton University Press, Princeton, N.J., 1967. MR 0214150, DOI 10.1515/9780691219615
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 99-104
- MSC: Primary 42B25; Secondary 47B38, 47D03
- DOI: https://doi.org/10.1090/S0002-9939-1991-1068123-9
- MathSciNet review: 1068123