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In this paper, we study the bilinear Littlewood-Paley square function introduced by M. Lacey. We give an easy proof of its boundedness from Lᵖ(Rᵈ) × Lq(Rᵈ) into Lʳ(Rᵈ),~d≥ 1, for all possible values of exponents $p,q,r,$ i.e. for 2≤ p,q≤ ∞ ,~1≤ r≤ ∞ satisfying 1/p+1/q= 1/r. We also prove analogous results for bilinear square functions on the torus group Tᵈ.
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Ratnakumar et al. (2012) studied this question.
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