zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Criteria on boundedness of matrix operators in weighted spaces of sequences and their applications. (English) Zbl 1225.26056
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.

26D15Inequalities for sums, series and integrals of real functions
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Full Text: EMIS EuDML