# Conditions on triangle inequality for integral kernel

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?

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