Mots-clés : Nikolskii–-Besov class
@article{IIGUM_2021_37_a5,
author = {G. I. Zelenov},
title = {On distributions of trigonometric polynomials in {Gaussian} random variables},
journal = {The Bulletin of Irkutsk State University. Series Mathematics},
pages = {77--92},
year = {2021},
volume = {37},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IIGUM_2021_37_a5/}
}
G. I. Zelenov. On distributions of trigonometric polynomials in Gaussian random variables. The Bulletin of Irkutsk State University. Series Mathematics, Tome 37 (2021), pp. 77-92. http://geodesic.mathdoc.fr/item/IIGUM_2021_37_a5/
[1] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, v. 1, 2, 2-e izd., Nauka, M., 1996, 480 pp.; Besov O. V., Il'in V.P., Nikol'ski{ĭ} S.M., Integral representations of functions and imbedding theorems, v. I, V. H. Winston Sons, Washington, 1978, viii+345 pp. ; v. II, Halsted Press [John Wiley Sons], New York–Toronto, 1979, viii+311 pp. | Zbl
[2] Bogachev V. I., Differentiable measures and the Malliavin calculus, Amer. Math. Soc., Rhode Island, Providence, 2010, 510 pp. | Zbl
[3] Bogachev V. I., “Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures”, Russian Math. Surveys, 71:4 (2016), 703–749 | DOI | Zbl
[4] Bogachev V. I., “Distributions of polynomials in many variables and Nikolskii-Besov spaces”, Real Anal. Exchange, 44:1 (2019), 49–63 | DOI
[5] Bogachev V. I., Kosov E. D., Popova S. N., “A new approach to Nikolskii–Besov classes”, Moscow Math. J., 19:4 (2019), 619–654 | DOI | Zbl
[6] Bogachev V., Kosov E., Zelenov G., “Fractional smoothness of distributions of polynomials and a fractional analog of the Hardy–Landau–Littlewood inequality”, Trans. Amer. Math. Soc., 370:6 (2018), 4401–4432 | DOI | Zbl
[7] Bogachev V. I., Zelenov G. I., Kosov E. D., “Membership of distributions of polynomials in the Nikolskii–Besov class”, Dokl. Math., 94:2 (2016), 453–457 | DOI | Zbl
[8] Carbery A., Wright J., “Distributional and $L^q$ norm inequalities for polynomials over convex bodies in $\mathbb R^n$”, Math. Research Letters, 8:3 (2001), 233–248 | DOI | Zbl
[9] Davydov Y. A., “On distance in total variation between image measures”, Statistics Probability Letters, 129 (2017), 393–400 | DOI | Zbl
[10] Kosov E. D., “Fractional smoothness of images of logarithmically concave measures under polynomials”, J. Math. Anal. Appl., 462:1 (2018), 390–406 | DOI | Zbl
[11] Kosov E. D., “Besov classes on finite and infinite dimensional spaces”, Sbornik Math., 210:5 (2019), 663–692 | DOI | Zbl
[12] Nazarov F. L., “Local estimates for exponential polynomials and their applications to inequalities of the uncertainty principle type”, St. Petersburg Math. J., 5:4 (1994), 663–717
[13] Nazarov F., Sodin M., Volberg A., “The geometric Kannan–Lovasz–Simonovits lemma, dimension-free estimates for the distribution of the values of polynomials, and the distribution of the zeros of random analytic functions”, St. Petersburg Math. J., 14:2 (2003), 351–366 | DOI | Zbl
[14] Nourdin I., Poly G., “Convergence in total variation on Wiener chaos”, Stochastic Process. Appl., 123:2 (2013), 651–674 | DOI | Zbl
[15] Zelenov G. I., “On distances between distributions of polynomials”, Theory Stoch. Processes, 22:2 (2017), 79–85 | Zbl
[16] Zelenov G. I., “Fractional smoothness of distributions of trigonometric polynomials on a space with a Gaussian measure”, The Bulletin of Irkutsk state University. Series Mathematics, 31 (2020), 78–95 (in Russian) | DOI | Zbl