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Zbl 1225.26056
Taspaganbetova, Zhanar; Temirkhanova, Ainur
Criteria on boundedness of matrix operators in weighted spaces of sequences and their applications. (English)
[J] Ann. Funct. Anal. AFA 2, No. 1, 114-127, electronic only (2011). ISSN 2008-8752/e

Summary: In this paper we prove a new discrete Hardy-type inequality involving a kernel which has a more general form than those known in the literature. We obtain necessary and sufficient conditions for the boundedness of a matrix operator from the weighted $l_{p,v}$ space into the weighted $l_{q,u}$ space defined by $$(Af)_j:=\sum^\infty_{i=1} a_{i,j} f_i,$$ for all $f=\{f_i\}^\infty_{i=1}\in L_{p,v}$ in case $1<q<p<\infty$ and $a_{i,j}\ge 0$. Then we deduce a corresponding dual statement.

MSC 2000:: *26D15 Inequalities for sums, series and integrals of real functions
47B37 Operators on sequence spaces, etc.

Keywords: inequalities; discrete Hardy-type inequalities; weights; matrix operators

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Zentralblatt MATH Berlin [Germany]