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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 H_p_(·)(R^d) and H_p_(·),_q(R^d) and about the θ-summability of multidimensional Fourier transforms. We prove that the maximal operator of the θ means is bounded from H_p_(·)(R^d) to L_p_(·)(R^d) and from H_p_(·),_q(R^d) to L_p(·),_q(R^d). 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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