%0 Journal Article
%T Potential Operators on Cones of Nonincreasing Functions
%A Alexander Meskhi
%A Ghulam Murtaza
%J Journal of Function Spaces and Applications
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/474681
%X Necessary and sufficient conditions on weight pairs guaranteeing the two-weight inequalities for the potential operators (¡Ò)()=¡Þ0(()/|£¿|1£¿) and (£¿1,2¡Ò)(,)=¡Þ0¡Ò¡Þ0((,)/|£¿|1£¿1|£¿|1£¿2) on the cone of nonincreasing functions are derived. In the case of £¿1,2, we assume that the right-hand side weight is of product type. The same problem for other mixed-type double potential operators is also studied. Exponents of the Lebesgue spaces are assumed to be between 1 and ∞.
%U http://www.hindawi.com/journals/jfsa/2012/474681/