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}
}
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

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