Variable Hardy and Hardy-Lorentz spaces and applications in Fourier analysis
DOI:
https://doi.org/10.24193/subbmath.2018.3.09Keywords:
Variable Hardy spaces, variable Hardy-Lorentz spaces, atomic decomposition, θ-summability, maximal operator.Abstract
We summarize some results about the variable Hardy and Hardy d d Lorentz spaces Hp(·)(R ) and Hp(·),q (R ) and about the θ-summability of multidimensional Fourier transforms. We prove that the maximal operator of the ... means is bounded from Hp(·)(R ) to Lp(·)(R ) and from Hp(·),q (R ) to Lp(·),q (R ). This implies some norm and almost everywhere convergence results for the Riesz, Bochner-Riesz, Weierstrass, Picard and Bessel summations.
Mathematics Subject Classification (2010): 42B08, 42A38, 42A24, 42B25, 42B30.
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