Maximal Singular Integral Transforms on Local Fields

We show that, on local fields, ``nice'' singular integral transforms preserve -spaces for <!-- MATH $0 < p < \infty$ --> <img width="99" height="37" align="MIDDLE" border="0" src="images/img7.gif" alt="$ 0 < p < \infty $"> where is the space of all distributions whose maximal functions are in . A version of the F. and M. Riesz theorem is also obtained.