Pankaj Jain
South Asian University, New Delhi, India

Starting from the classical Sawyer's duality principle that deals with the duality of weighted Lebesgue spaces $L^p_v$ for non-negative non-increasing functions, in this talk, we shall discuss this principle for weighted grand Lebesgue spaces $L^{p}_v$. As applications to these principles, we shall derive boundedness of various integral operators on the cone of monotone functions.