| Title:
|
Some inequalities involving upper bounds for some matrix operators. I (English) |
| Author:
|
Lashkaripour, R. |
| Author:
|
Foroutannia, D. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
553-572 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider the problem of finding upper bounds of certain matrix operators such as Hausdorff, Nörlund matrix, weighted mean and summability on sequence spaces $l_p(w)$ and Lorentz sequence spaces $d(w,p)$, which was recently considered in [9] and [10] and similarly to [14] by Josip Pecaric, Ivan Peric and Rajko Roki. Also, this study is an extension of some works by G. Bennett on $l_p$ spaces, see [1] and [2]. (English) |
| Keyword:
|
inequality |
| Keyword:
|
norm |
| Keyword:
|
summability matrix |
| Keyword:
|
Hausdorff matrix |
| Keyword:
|
Nörlund matrix |
| Keyword:
|
weighted mean matrix |
| Keyword:
|
weighted sequence space and Lorentz sequence space |
| MSC:
|
15A45 |
| MSC:
|
15A60 |
| MSC:
|
47-99 |
| MSC:
|
47A99 |
| MSC:
|
47B37 |
| idZBL:
|
Zbl 1174.15017 |
| idMR:
|
MR2337614 |
| . |
| Date available:
|
2009-09-24T11:47:33Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128189 |
| . |
| Reference:
|
[1] G. Bennett: Factorizing the classical inequalities.Mem. Amer. Math. Soc. 576 (1996), 1–130. Zbl 0857.26009, MR 1317938 |
| Reference:
|
[2] G. Bennett: Inequalities complimentary to Hardy.Quart. J. Math. Oxford (2) 49 (1998), 395–432. Zbl 0929.26013, MR 1652236 |
| Reference:
|
[3] D. Borwein and F. P. Cass: Nörlund matrices as bounded operators on $l_p$.Arch. Math. 42 (1984), 464–469. MR 0756700, 10.1007/BF01190697 |
| Reference:
|
[4] D. Borwein: Nörlund operators on $l_p$.Canada. Math. Bull. 36 (1993), 8–14. MR 1205888, 10.4153/CMB-1993-002-x |
| Reference:
|
[5] G. H. Hardy: An inequality for Hausdorff means.J. London Math. Soc. 18 (1943), 46–50. Zbl 0061.12704, MR 0008854 |
| Reference:
|
[6] G. H. Hardy: Divergent Series.2nd edition, American Mathematical Society, 2000. |
| Reference:
|
[7] G. H. Hardy and J. E. Littlewood: A maximal theorem with function-theoretic.Acta Math. 54 (1930), 81–116. MR 1555303, 10.1007/BF02547518 |
| Reference:
|
[8] G. H. Hardy, J. E. Littlewood and G. Polya: Inequalities.2nd edition, Cambridge University press, Cambridge, 2001. MR 0944909 |
| Reference:
|
[9] G. J. O. Jameson and R. Lashkaripour: Lower bounds of operators on weighted $l_p$ spaces and Lorentz sequence spaces.Glasgow Math. J. 42 (2000), 211–223. MR 1763740, 10.1017/S0017089500020061 |
| Reference:
|
[10] G. J. O. Jameson and R. Lashkaripour: Norms of certain operators on weighted $l_p$ spaces and Lorentz sequence spaces.J. Inequalities in Pure and Applied Mathematics, 3, Issue 1, Article 6 (2002). MR 1888921 |
| Reference:
|
[11] R. Lashkaripour: Lower bounds and norms of operators on Lorentz sequence spaces.Doctoral dissertation (Lancaster, 1997). |
| Reference:
|
[12] R. Lashkaripour: Transpose of the Weighted Mean operators on Weighted Sequence Spaces.WSEAS Transaction on Mathematics, Issue 4, 4 (2005), 380–385. MR 2119309 |
| Reference:
|
[13] R. Lashkaripour and D. Foroutannia: Lower Bounds for Matrices on Weighted Sequence Spaces.Journal of Sciences Islamic Republic of IRAN, 18 (2007), 49–56. MR 2499829 |
| Reference:
|
[14] J. Pecaric, I. Peric and R. Roki: On bounds for weighted norms for matrices and integral operators.Linear Algebra and Appl. 326 (2001), 121–135. MR 1815954 |
| . |
