We consider the study
of the tent spaces over general (possibly tangential) approach regions and
their atomic decomposition. As a consequence, we obtain some pointwise
estimates for a class of operators, using the duality properties of a certain
type of Carleson measures. In particular, we can get the boundedness of a
family of bilinear operators defined on the product of Lq and some space of
measures, into a Lipschitz space; we give yet another proof of the pointwise
boundedness for the Fourier transform of distributions in Hp and we improve
and generalize the Féjer-Riesz inequality for harmonic extensions of Hp
functions.
