# Marcinkiewicz- $$\theta$$ -Summability of Fourier Transforms

@article{Weisz2002Marcinkiewicz, title={Marcinkiewicz- \$\$\theta\$\$ -Summability of Fourier Transforms}, author={Ferenc Weisz}, journal={Acta Mathematica Hungarica}, year={2002}, volume={96}, pages={149-160} }

- Published 2002
DOI:10.1023/A:1015673914063

AbstractA general summability method of two-dimensional Fourier transforms is given with the help of an integrable function
$$\theta$$
. Under some conditions on
$$\theta$$
we show that the maximal operator of the Marcinkiewicz-
$$\theta$$
-means of a tempered distribution is bounded from
$$H_p \left( {R^2 } \right)$$
to
$$L_p \left( {R^2 } \right)$$
for all
$$p_0 < p \leqq \infty $$
and, consequently, is of weak type
$$\left( {1,1} \right)$$
, where
$$p_0 < 1$$
depends only on… CONTINUE READING