1 Introduction ................................................. 5
2 Preliminaries ................................................ 8
2.1 RD-spaces ............................................... 8
2.2 Variable exponent Lebesgue spaces ....................... 9
2.3 Boundedness of the Hardy-Littlewood maximal operator ... 10
3 Hardy spaces with variable exponents ........................ 14
3.1 Hardy spaces with variable exponents via the grand
maximal function ....................................... 14
3.2 Hardy spaces with variable exponents via the
non-tangential maximal function ........................ 16
3.3 Hardy spaces with variable exponents via the dyadic
maximal function ....................................... 18
3.4 Relations between (G 0(β1, γ1) and (G0(β2, γ2))' ....... 22
4 Atomic characterizations .................................... 24
4.1 Atomic Hardy spaces with variable exponents ............ 24
4.2 Auxiliary estimates for the proof of Theorem 4.3 ....... 26
4.3 Proof of Theorem 4.3 ................................... 30
4.4 Some consequences of the atomic characterization ....... 36
4.5 Finite atomic characterizations ........................ 39
5 Characterizations in terms of Littlewood-Paley functions .... 47
5.1 Main results ........................................... 47
5.2 Proofs of main results of Section 5.1 .................. 49
6 Applications ................................................ 57
6.1 Fractional integral operators and Olsen's inequality ... 57
6.2 Singular integral operators ............................ 62
6.3 Quasi-Banach valued sublinear operators ................ 65
7 Duality of H*,р(•)(Χ) with p+ (0,1] ......................... 66
References .................................................. 70
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