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Apv Aqw 0 q p 00
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Ap(v Aq(w Assume assumptions of Lemma assumptions of Theorem Boundedness of S,7;A characterize the validity classical and weak-type classical Hardy-Littlewood maximal classical Lorentz spaces coincides Consequently cube Q define domain in Rn EOP1 EOP2 f G M(Rn following statements follows on applying fractional maximal operator function space G Rn Hardy-Littlewood maximal operator holds on M+(0 implies inequalities 5.4 inequality 4.9 inequality 7.3 Interpolation of Operators ip G Lebesgue space Let 7 G Let Q Lorentz-Zygmund space mapped by M7 maximal operator M7 Moreover necessary and sufficient non-increasing rearrangement numbers Opic Orlicz space positive constant proof of Lemma Proof of Theorem Q C Rn q G 1,oo quasi-norms Real interpolation Remark result follows Riesz potential satisfied scales of spaces spaces close statements are equivalent sufficient conditions supremum Theorem 4.1 validity of inequalities verify weak type weak-type Lorentz spaces weighted inequalities