A weak type $(p,a)$ criterion for operators, and applications

Bernhard H. Haak, El-Maati Ouhabaz

Let $(X,d,\hat{I}¼)$ be a space of homogeneous type and $\hat{I}\text{c◯}$ an open subset of $X$. Given a bounded operator $T:L^p(\hat{I}\text{c◯})\to L^q(\hat{I}\text{c◯})$ for some $1\le p\le q<\infty$, we give a crite…