Weak-type operator
= Weak-type operator
{title2=$\mu\{|Sf|>\lambda\}\leq(C\|f\|_p/\lambda)^q$}
An operator has weak type $(p,q)$, with finite $q$, if the displayed bound holds for every input and every $\lambda>0$, with one constant independent of both. It controls the distribution of its output rather than requiring its strong $L^q$ <norm> to be finite.