Volume 3,  Issue 1, 2002

Article 6

NORMS OF CERTAIN OPERATORS ON WEIGHTED SPACES AND LORENTZ SEQUENCE SPACES

G.J.O. JAMESON AND R. LASHKARIPOUR

DEPARTMENT OF MATHEMATICS AND STATISTICS, 
LANCASTER UNIVERSITY 
LANCASTER LA1 4YF, 
GREAT BRITAIN. 
E-Mail: g.jameson@lancaster.ac.uk

FACULTY OF SCIENCE,
UNIVERSITY OF SISTAN AND BALUCHISTAN, 
ZAHEDAN, IRAN.
E-Mail: lashkari@hamoon.usb.ac.ir

Received 07 May, 2001; 21 September, 2001.
Communicated by: B. Opic

ABSTRACT.    The problem addressed is the exact determination of the norms of the classical Hilbert, Copson and averaging operators on weighted $\ell_p$ spaces and the corresponding Lorentz sequence spaces $d(w,p)$, with the power weighting sequence $w_n = n^{-\alpha }$ or the variant defined by $w_1+ \cdots +w_n = n^{1-\alpha }$. Exact values are found in each case except for the averaging operator with $w_n = n^{-\alpha }$, for which estimates deriving from various different methods are obtained and compared.
Key words:
Hardy's inequality, Hilbert's inequality, Norms of operators.

2000 Mathematics Subject Classification:
26D15, 15A60, 47B37.

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