Estimates for bilinear generalized fractional integral operator and its commutator on generalized Morrey spaces over RD-spaces

Let (X,d,μ ) be an RD-space. In this paper, we prove that a bilinear generalized fractional integral T_α is bounded from the product of generalized Morrey spaces ℒ^φ _1,p_1(X)×ℒ^φ _2,p_2(X) into spaces ℒ^φ ,q(X) , and it is also bounded from the product of spaces ℒ^φ _1,p_1(X)×ℒ^φ _2,p_2(X) into generalized weak Morrey spaces Wℒ^φ ,q(X) , where the Lebesgue measurable functions φ _1, φ _2 and φ satisfy certain conditions and φ _1φ _2=φ , α∈ (0,1) and 1/q=1/p_1+1/p_2-2α for 1更多