We summarize some results about the variable Hardy and Hardy- Lorentz spaces Hp(·)(ℝd) and Hp(·),q(ℝd) and about the θ-summability of multidimensional Fourier transforms. We prove that the maximal operator of the - means is bounded from Hp(·)(ℝd) to Lp(·)(ℝd) and from Hp(·);q(ℝd) to Lp(·);q(ℝd). This implies some norm and almost everywhere convergence results for the Riesz, Bochner-Riesz, Weierstrass, Picard and Bessel summations.
- Atomic decomposition
- Maximal operator
- Variable Hardy spaces
- Variable Hardy-Lorentz spaces
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