Abstract
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.
Similar content being viewed by others
References
G. Bennett: Factorizing the Classical Inequalities. Mem. Amer. Math. Soc. 576, 1996.
D. Foroutannia, R. Lashkaripour: Lower bounds for summability matrices on weighted sequence spaces. Lobachevskii J. Math 27 (2007), 15–29.
G. H. Hardy, J. E. Littlewood, G. Pólya: Inequalities, 2nd edition. Cambridge University Press, Cambridge, 1988.
G. J. O. Jameson, R. Lashkaripour: Lower bounds of operators on weighted l p spaces and Lorentz sequence spaces. Glasg. Math. J. 42 (2000), 211–223.
G. J. O. Jameson, R. Lashkaripour: Norms of certain operators on weighted l p spaces and Lorentz sequence spaces. JIPAM, J. Inequal. Pure Appl. Math. 3 (2002). Electronic only.
R. Lashkaripour, D. Foroutannia: Inequalities involving upper bounds for certain matrix operators. Proc. Indian Acad. Sci., Math. Sci. 116 (2006), 325–336.
R. Lashkaripour, D. Foroutannia: Norm and lower bounds of operators on weighted sequence spaces. Math. Vesn. 59 (2007), 47–56.
R. Lashkaripour, D. Foroutannia: Some inequalities involving upper bounds for some matrix operators I. Czechoslovak Math. J 57 (2007), 553–572.
J. Pečarić, I. Perić, R. Roki: On bounds for weighted norms for matrices and integral operators. Linear Algebra Appl. 326 (2001), 121–135.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lashkaripour, R., Foroutannia, D. Lower bounds for matrices on block weighted sequence spaces I. Czech Math J 59, 81–94 (2009). https://doi.org/10.1007/s10587-009-0006-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10587-009-0006-6