  We prove fractional Sobolev-Poincar\'e inequalities, capacitary versions of
fractional Poincar\'e inequalities, and pointwise and localized fractional
Hardy inequalities in a metric space equipped with a doubling measure. Our
results generalize and extend earlier work where such inequalities have been
considered in the Euclidean spaces or in the non-fractional setting in metric
spaces. The results concerning pointwise and localized variants of fractional
Hardy inequalities are new even in the Euclidean case.
