Geodesic
Bounded Toeplitz and Hankel productson weighted Bergman spaces of the unit ball
Małgorzata Michalska 1   ; Maria Nowak 2   ; Pawe/l Sobolewski 3
1 Institute of Mathematics Maria Curie-Skłodowska University 20-031 Lublin, Poland
2 Institute of Mathematics Mariae Curie-Skłodowska University 20-031 Lublin, Poland
3 Institute of Mathematics Mariae Curie-Sk/lodowska University 20-031 Lublin, Poland
Annales Polonici Mathematici, Tome 99 (2010) no. 1, pp. 45-53 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We prove a sufficient condition for products of Toeplitz operators $T_fT_{\bar g}$, where $f,g$ are square integrable holomorphic functions in the unit ball in $\mathbb C^n$, to be bounded on the weighted Bergman space. This condition slightly improves the result obtained by K. Stroethoff and D. Zheng. The analogous condition for boundedness of products of Hankel operators $H_fH^*_g$ is also given.
DOI : 10.4064/ap99-1-4
Keywords: prove sufficient condition products toeplitz operators bar where square integrable holomorphic functions unit ball mathbb bounded weighted bergman space condition slightly improves result obtained stroethoff zheng analogous condition boundedness products hankel operators * given

Małgorzata Michalska  1   ; Maria Nowak  2   ; Pawe/l Sobolewski  3

1 Institute of Mathematics Maria Curie-Skłodowska University 20-031 Lublin, Poland
2 Institute of Mathematics Mariae Curie-Skłodowska University 20-031 Lublin, Poland
3 Institute of Mathematics Mariae Curie-Sk/lodowska University 20-031 Lublin, Poland 
@article{10_4064_ap99_1_4,
     author = {Ma{\l}gorzata Michalska and Maria Nowak and Pawe/l Sobolewski},
     title = {Bounded {Toeplitz} and {Hankel} productson weighted {Bergman} spaces of the unit ball},
     journal = {Annales Polonici Mathematici},
     pages = {45--53},
     year = {2010},
     volume = {99},
     number = {1},
     doi = {10.4064/ap99-1-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap99-1-4/}
}
TY  - JOUR
AU  - Małgorzata Michalska
AU  - Maria Nowak
AU  - Pawe/l Sobolewski
TI  - Bounded Toeplitz and Hankel productson weighted Bergman spaces of the unit ball
JO  - Annales Polonici Mathematici
PY  - 2010
SP  - 45
EP  - 53
VL  - 99
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap99-1-4/
DO  - 10.4064/ap99-1-4
LA  - en
ID  - 10_4064_ap99_1_4
ER  - 
%0 Journal Article
%A Małgorzata Michalska
%A Maria Nowak
%A Pawe/l Sobolewski
%T Bounded Toeplitz and Hankel productson weighted Bergman spaces of the unit ball
%J Annales Polonici Mathematici
%D 2010
%P 45-53
%V 99
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/ap99-1-4/
%R 10.4064/ap99-1-4
%G en
%F 10_4064_ap99_1_4
Małgorzata Michalska; Maria Nowak; Pawe/l Sobolewski. Bounded Toeplitz and Hankel productson weighted Bergman spaces of the unit ball. Annales Polonici Mathematici, Tome 99 (2010) no. 1, pp. 45-53. doi: 10.4064/ap99-1-4

Cité par Sources :