Geodesic
On Weighted Norms of Riesz Transforms Equal to One
Matematičeskie zametki, Tome 72 (2002) no. 6, pp. 869-882

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

We consider the vector Riesz transform $\nabla ^t\Delta ^{-(t+s)/2}\operatorname {div}^s$ of even order $s+t$ in the weighted space$L_2(\mathbb R^n;|x|^a)$. We establish that for $t\ne s$, $n>3$ its norm is equal to one on some interval of values of $a$, while inside the interval a stronger estimate for a subordinate norm is valid. 
@article{MZM_2002_72_6_a7,
     author = {E. A. Kalita},
     title = {On {Weighted} {Norms} of {Riesz} {Transforms} {Equal} to {One}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {869--882},
     publisher = {mathdoc},
     volume = {72},
     number = {6},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a7/}
}
TY  - JOUR
AU  - E. A. Kalita
TI  - On Weighted Norms of Riesz Transforms Equal to One
JO  - Matematičeskie zametki
PY  - 2002
SP  - 869
EP  - 882
VL  - 72
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a7/
LA  - ru
ID  - MZM_2002_72_6_a7
ER  - 
%0 Journal Article
%A E. A. Kalita
%T On Weighted Norms of Riesz Transforms Equal to One
%J Matematičeskie zametki
%D 2002
%P 869-882
%V 72
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a7/
%G ru
%F MZM_2002_72_6_a7
E. A. Kalita. On Weighted Norms of Riesz Transforms Equal to One. Matematičeskie zametki, Tome 72 (2002) no. 6, pp. 869-882. http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a7/