  This paper is concerned with a class of singular stable-like Dirichlet forms
on $\R^d$, which are generated by $d$ independent copies of a one-dimensional
symmetric $\alpha$-stable process, and whose L\'evy jump kernel measure is
concentrated on the union of the coordinate axes. Explicit and sharp criteria
for Poincar\'e inequality, super Poincar\'e inequality and weak Poincar\'e
inequality of such singular Dirichlet forms are presented. When the reference
measure is a product measure on $\R^d$, we also consider the entropy inequality
for the associated Dirichlet forms, which is similar to the log-Sobolev
inequality for local Dirichlet forms, and enjoys the tensorisation property.
