| Title:
|
Lower bounds for matrices on block weighted sequence spaces. I (English) |
| Author:
|
Lashkaripour, R. |
| Author:
|
Foroutannia, D. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
81-94 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider some matrix operators on block weighted sequence spaces $l_p(w,F)$. The problem is to find the lower bound of some matrix operators such as Hausdorff and Hilbert matrices on $l_p(w,F)$. This study is an extension of papers by G. Bennett, G.J.O. Jameson and R. Lashkaripour. (English) |
| Keyword:
|
block weighted sequence spaces |
| Keyword:
|
lower bound |
| Keyword:
|
inequality |
| Keyword:
|
Hausdorff matrix |
| Keyword:
|
Hilbert matrix |
| MSC:
|
26D15 |
| MSC:
|
46B45 |
| MSC:
|
47B37 |
| idZBL:
|
Zbl 1217.47065 |
| idMR:
|
MR2486617 |
| . |
| Date available:
|
2010-07-20T14:53:44Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140465 |
| . |
| Reference:
|
[1] Bennett, G.: Factorizing the Classical Inequalities.Mem. Amer. Math. Soc. 576 (1996). Zbl 0857.26009, MR 1317938 |
| Reference:
|
[2] Foroutannia, D., Lashkaripour, R.: Lower bounds for summability matrices on weighted sequence spaces.Lobachevskii J. Math 27 (2007), 15-29. Zbl 1158.47021, MR 2396994 |
| Reference:
|
[3] Hardy, G. H., Littlewood, J. E., Pólya, G.: Inequalities, 2nd edition.Cambridge University Press Cambridge (1988). MR 0944909 |
| Reference:
|
[4] Jameson, G. J. O., Lashkaripour, R.: Lower bounds of operators on weighted $l_p$ spaces and Lorentz sequence spaces.Glasg. Math. J. 42 (2000), 211-223. MR 1763740, 10.1017/S0017089500020061 |
| Reference:
|
[5] Jameson, G. J. O., Lashkaripour, R.: Norms of certain operators on weighted $l_p$ spaces and Lorentz sequence spaces.JIPAM, J. Inequal. Pure Appl. Math. 3 (2002), Electronic only. Zbl 1021.47019, MR 1888921 |
| Reference:
|
[6] Lashkaripour, R., Foroutannia, D.: Inequalities involving upper bounds for certain matrix operators.Proc. Indian Acad. Sci., Math. Sci. 116 (2006), 325-336. Zbl 1118.47024, MR 2256009, 10.1007/BF02829749 |
| Reference:
|
[7] Lashkaripour, R., Foroutannia, D.: Norm and lower bounds of operators on weighted sequence spaces.Math. Vesn. 59 (2007), 47-56. MR 2328828 |
| Reference:
|
[8] Lashkaripour, R., Foroutannia, D.: Some inequalities involving upper bounds for some matrix operators I.Czechoslovak Math. J 57 (2007), 553-572. Zbl 1174.15017, MR 2337614 |
| Reference:
|
[9] Pečarić, J., Perić, I., Roki, R.: On bounds for weighted norms for matrices and integral operators.Linear Algebra Appl. 326 (2001), 121-135. MR 1815954 |
| . |
