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block weighted sequence spaces; lower bound; inequality; Hausdorff matrix; Hilbert matrix
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.
[1] Bennett, G.: Factorizing the Classical Inequalities. Mem. Amer. Math. Soc. 576 (1996). MR 1317938 | Zbl 0857.26009
[2] Foroutannia, D., Lashkaripour, R.: Lower bounds for summability matrices on weighted sequence spaces. Lobachevskii J. Math 27 (2007), 15-29. MR 2396994 | Zbl 1158.47021
[3] Hardy, G. H., Littlewood, J. E., Pólya, G.: Inequalities, 2nd edition. Cambridge University Press Cambridge (1988). MR 0944909
[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. DOI 10.1017/S0017089500020061 | MR 1763740
[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. MR 1888921 | Zbl 1021.47019
[6] Lashkaripour, R., Foroutannia, D.: Inequalities involving upper bounds for certain matrix operators. Proc. Indian Acad. Sci., Math. Sci. 116 (2006), 325-336. DOI 10.1007/BF02829749 | MR 2256009 | Zbl 1118.47024
[7] Lashkaripour, R., Foroutannia, D.: Norm and lower bounds of operators on weighted sequence spaces. Math. Vesn. 59 (2007), 47-56. MR 2328828
[8] Lashkaripour, R., Foroutannia, D.: Some inequalities involving upper bounds for some matrix operators I. Czechoslovak Math. J 57 (2007), 553-572. MR 2337614 | Zbl 1174.15017
[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
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