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    STUDIA MATHEMATICA - Issue no. 3 / 2018  
         
  Article:   VARIABLE HARDY AND HARDY-LORENTZ SPACES AND APPLICATIONS IN FOURIER ANALYSIS.

Authors:  FERENC WEISZ.
 
       
         
  Abstract:  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 θ 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. 

Mathematics Subject Classification (2010): 42B08, 42A38, 42A24, 42B25, 42B30. 
Keywords: Variable Hardy spaces, variable Hardy-Lorentz spaces, atomic decomposition, θ-summability, maximal operator
 
         
     
         
         
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