“…For the Lebesgue space L p (p ≥ 1) and the Hardy space H 1 , the boundedness of H Φ (even H Φ,A ) are well established (see [4,7,19,20,23,24,27,30,35]). Besides spaces L p and H 1 , the boundedness of H Φ on other function spaces was recently also studied by many authors (see, for instance, [5,15,22,26,31,32,36,37] and the references therein).…”