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Weighted Norm Inequalities of Hardy Type for a Class of Integral Operators
Author(s) -
Stepanov Vladimir D
Publication year - 1994
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/50.1.105
Subject(s) - mathematics , norm (philosophy) , monotone polygon , pure mathematics , inequality , kernel (algebra) , class (philosophy) , type (biology) , combinatorics , discrete mathematics , mathematical analysis , ecology , artificial intelligence , computer science , biology , geometry , political science , law
Necessary and sufficient conditions for the boundedness fromL υ p ( R + ) toL u p ( R + ) of Volterra integral operators of the formK f ( x ) = ∫ 0 x k ( x , y ) f ( y ) d y , where k ( x,y ) is a non‐negative kernel under suitable monotone conditions, are given. The cases 1 < p ⩽ q < ∞, 1 < q < p < ∞ and 0 < q < l < p < ∞ are considered. The results extend the well‐known weighted norm Hardy inequality.