Geodesic
Two-sided estimates of norms of a class of matrix operators
Matematičeskie trudy, Tome 24 (2021) no. 2, pp. 37-45.

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

In the article, we establish necessary and sufficient conditions for the validity of a discrete Hardy type inequality $$ \left(\sum\limits_{n=1}^{\infty}|(Af)_n|^q\right)^{\frac{1}{q}} \le C\left(\sum\limits_{k=1}^{\infty}|f_k|^p\right)^{\frac{1}{p}} $$ for one class of matrix operators $$(Af)_n=\sum\limits_{k=1}^{n}a_{n,k}f_k, n\ge 1,$$ for $1$. 
@article{MT_2021_24_2_a2,
     author = {A. A. Kalybay},
     title = {Two-sided estimates of norms of a class of matrix operators},
     journal = {Matemati\v{c}eskie trudy},
     pages = {37--45},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2021_24_2_a2/}
}
TY  - JOUR
AU  - A. A. Kalybay
TI  - Two-sided estimates of norms of a class of matrix operators
JO  - Matematičeskie trudy
PY  - 2021
SP  - 37
EP  - 45
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2021_24_2_a2/
LA  - ru
ID  - MT_2021_24_2_a2
ER  - 
%0 Journal Article
%A A. A. Kalybay
%T Two-sided estimates of norms of a class of matrix operators
%J Matematičeskie trudy
%D 2021
%P 37-45
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2021_24_2_a2/
%G ru
%F MT_2021_24_2_a2
A. A. Kalybay. Two-sided estimates of norms of a class of matrix operators. Matematičeskie trudy, Tome 24 (2021) no. 2, pp. 37-45. http://geodesic.mathdoc.fr/item/MT_2021_24_2_a2/

[1] Oinarov R., “Dvustoronnie otsenki normy nekotorykh klassov integralnykh operatorov”, Trudy MI RAN, 204, 1993, 240–250 | Zbl

[2] Oinarov R., Shalginbaeva S., “Vesovaya additivnaya otsenka odnogo klassa matrichnykh operatorov”, Izvestiya NAN RK, 2004, no. 1, 39–49

[3] Bennett G., “Some elementary inequalities”, Quart. J. Math. Oxford Ser., 38:152 (1987), 401–425 | DOI | Zbl

[4] Bennett G., “Some elementary inequalities. II”, Quart. J. Math. Oxford Ser., 39:156 (1988), 385–400 | DOI | Zbl

[5] Bennett G., “Some elementary inequalities. III”, Quart. J. Math. Oxford Ser., 42:166 (1991), 149–174 | DOI | Zbl

[6] Braverman M. Sh., Stepanov V. D., “On the discrete Hardy inequality”, Bull. London Math. Soc., 26 (1994), 283–287 | DOI | Zbl

[7] Kalybay A., Oinarov R., Temirkhanova A., “Boundedness of $n$-multiple discrete Hardy operators with weights for $1 q p \infty$”, J. Funct. Spaces Appl., 2013 | DOI | Zbl

[8] Oinarov R., Okpoti C. A., Persson L.-E., “Weighted inequalities of Hardy type for matrix operators: The case $q {} p$”, Math. Inequal. Appl., 10:4 (2007), 843–861 | Zbl

[9] Oinarov R., Taspaganbetova Z., “Criteria of boundedness and compactness of a class of matrix operators”, J. Ineq. Appl., 53 (2012), 2012–53 | DOI | Zbl

[10] Taspaganbetova Z., Temirkhanova A. M., “Criteria on boundedness of matrix operators in weighted spaces of sequences and their applications”, Ann. Funct. Anal., 2:1 (2011), 114–127 | DOI | Zbl