Abstract
In this article, we consider the bilinear operator T satisfying that there exists a positive constant C(T), depending on T, such that, for any measurable functions f and g with compact support, t∈ℝ with 0<|t|≤1, and x∈ℝn with 0∉supp(f(x−t⋅))∩supp(g(x−⋅)), T(f,g)(x)≤C(T)∫ℝnf(x−ty)g(x−y)|y|ndy. We investigate the boundedness of T on the vanishing generalized Morrey spaces V0Lp,φ(ℝn) and V∞Lp,φ(ℝn), and the boundedness of the subbilinear maximal operator ℳ on the vanishing generalized Morrey space V(∗)Lp,φ(ℝn), and their applications to some classical (sub)bilinear operators in harmonic analysis. As a byproduct, we also show that T is bounded on generalized Morrey spaces Lp,φ(ℝn). Some typical examples for the main results of this paper are also included.
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