Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent

Cheung, Ka Luen ; Ho, Kwok-Pun

Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 159-171

Abstract (VO)

The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block space with variable exponents. We find that the Hardy-Littlewood maximal operator is bounded on the block space with variable exponents whenever the Hardy-Littlewood maximal operator is bounded on the corresponding Lebesgue space with variable exponents.

Détail

DOI : 10.1007/s10587-014-0091-z

Classification : 42B25, 46E30
Keywords: block space; variable exponent analysis; Hardy-Littlewood maximal operator

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