On Weighted Norm Inequalities for Positive Linear Operators
نویسندگان
چکیده
Let T be a positive linear operator defined for nonnegative functions on a rj-finite measure space {X,m,fi). Given 1 < p < oo and a nonnegative weight function w on X , it is shown that there exists a nonnegative weight function v , finite /¿-almost everywhere on X , such that (1) I \Tf)*wdfi< j fvd/i, for all/>0, J x J x tere exists posi ( h if and only if th tive /¿-almost everywhere on X with (2) / {T(t>)pwdßl~pT'[(T(t>)P~]w] in (1). This partially answers a question of B. Muckenhoupt in [5]. Applications to some specific operators are also given.
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