Geodesic
Inequalities between the norms of a function and its derivatives
Eurasian mathematical journal, Tome 7 (2016) no. 1, pp. 28-49

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

The paper is devoted to the problem of finding the maximum of the norm $||x||_q$ with the constraints $||x||_p=\eta$, $||\dot{x}||_r=\sigma$, $x(0)=a$, $a, \sigma, \eta>0$, for functions $x\in L_p(\mathbb{R}_-)$ with derivatives $\dot{x}\in L_r(\mathbb{R_-})$, $0 p \leqslant q \infty$, $r > 1$. The arguments employed are based on the standard machinery of the calculus of variations. 
@article{EMJ_2016_7_1_a2,
     author = {A. S. Kochurov},
     title = {Inequalities between the norms of a function and its derivatives},
     journal = {Eurasian mathematical journal},
     pages = {28--49},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2016_7_1_a2/}
}
TY  - JOUR
AU  - A. S. Kochurov
TI  - Inequalities between the norms of a function and its derivatives
JO  - Eurasian mathematical journal
PY  - 2016
SP  - 28
EP  - 49
VL  - 7
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2016_7_1_a2/
LA  - en
ID  - EMJ_2016_7_1_a2
ER  - 
%0 Journal Article
%A A. S. Kochurov
%T Inequalities between the norms of a function and its derivatives
%J Eurasian mathematical journal
%D 2016
%P 28-49
%V 7
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2016_7_1_a2/
%G en
%F EMJ_2016_7_1_a2
A. S. Kochurov. Inequalities between the norms of a function and its derivatives. Eurasian mathematical journal, Tome 7 (2016) no. 1, pp. 28-49. http://geodesic.mathdoc.fr/item/EMJ_2016_7_1_a2/