Consider $\int_RK(x,y)f(y)dy$, where $K(x,y) \in M_+(R^2)$.

Let $L(t,s)$ be an iterated rearrangement of $K$. Let also $$ A(t,v)=\int_0^{1/v}L(1/t,s)ds, $$ which is decreasing with $v$ and increasing with $t$.

What conditions on $L$ would guarantee that $A(t,v)\leq A(t,u)+A(u,v)$ with $v<u<t$?

For example, if $L=1/t+s$ the condition would be specified. I am looking for more general answer.


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