Geodesic
Estimates for integral norms of polynomials on spaces with convex measures
Sbornik. Mathematics, Tome 206 (2015) no. 8, pp. 1030-1048

Voir la notice de l'article provenant de la source Math-Net.Ru

We show that measurable polynomials of degree $d$ are integrable to every positive power and all their $L^p$-norms are equivalent. We also prove a zero-one law for level sets of measurable polynomials and for sets of convergence of measurable polynomials of fixed degree on spaces with convex measures. We obtain an estimate for the $L^1$-norm of continuous polynomials in terms of the $L^1$-norm of their restriction to any set of positive measure. Bibliography: 19 titles.
Keywords: convex measures, logarithmically convex measures, measurable polynomials. 
@article{SM_2015_206_8_a0,
     author = {L. M. Arutyunyan and E. D. Kosov},
     title = {Estimates for integral norms of polynomials on spaces with convex measures},
     journal = {Sbornik. Mathematics},
     pages = {1030--1048},
     publisher = {mathdoc},
     volume = {206},
     number = {8},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2015_206_8_a0/}
}
TY  - JOUR
AU  - L. M. Arutyunyan
AU  - E. D. Kosov
TI  - Estimates for integral norms of polynomials on spaces with convex measures
JO  - Sbornik. Mathematics
PY  - 2015
SP  - 1030
EP  - 1048
VL  - 206
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2015_206_8_a0/
LA  - en
ID  - SM_2015_206_8_a0
ER  - 
%0 Journal Article
%A L. M. Arutyunyan
%A E. D. Kosov
%T Estimates for integral norms of polynomials on spaces with convex measures
%J Sbornik. Mathematics
%D 2015
%P 1030-1048
%V 206
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2015_206_8_a0/
%G en
%F SM_2015_206_8_a0
L. M. Arutyunyan; E. D. Kosov. Estimates for integral norms of polynomials on spaces with convex measures. Sbornik. Mathematics, Tome 206 (2015) no. 8, pp. 1030-1048. http://geodesic.mathdoc.fr/item/SM_2015_206_8_a0/