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

Bernhard H. Haak, El-Maati Ouhabaz

Let $(X,d,\mu )$ be a space of homogeneous type and $\Omega$ an open subset of $X$. Given a bounded operator $T:L^p(\Omega )\to L^q(\Omega )$ for some $1\le p\le q<\infty$, we give a criterion…