Multiple weighted estimates for bilinear Calderon-Zygmund operator and its commutator on non-homogeneous spaces

Let (chi, d, mu) be a non-homogeneous metric measure space. In this setting, the author proves that the bilinear Calderon-Zygmund operator (T) over tilde is bounded from the product of weighted Morrey spaces L-omega 1(p1,kappa)(mu) x L-omega 2(p2,kappa)(mu) into weighted weak Morrey spaces WL nu(omega) over right arrowp,kappa(mu), and it is also bounded from the product of generalized weighted Morrey spaces L-omega 1(p1,phi 1)(mu) x L-omega 2(p2,phi 2)(mu) into generalized weighted weak Morrey spaces L-omega 1(nu(omega) over right arrow)p,phi(mu), where (omega) over right arrow=(omega(1), omega(2)), rho is an element of[1, infinity), (omega) over right arrow is an element of A((P) over right arrow)(rho)(mu), (P) over right arrow=(p(1), p(2)) satisfying 1/p = 1/p(1) + 1/p(2) for 1 <= p(1), p(2) < infinity. Furthermore, via the sharp maximal estimate for the commutator <(T)over tilde>(b1,b2) which is generated by b(1), b(2) is an element of (RBMO) over tilde(mu) and (T) over tilde, the author shows that (T) over tilde (b1,b2) is bounded from the product of spaces L-omega 1(p1,kappa)(mu) x L-omega 2(p2,kappa)(mu) into spaces WL nu(omega) over right arrowp,kappa(mu), and it is also bounded from the product of spaces L-omega 1(p1,phi 1)(mu) x L-omega 2(p2,phi 2)(mu) into spaces WL nu(omega) over right arrowp,phi(mu). (c) 2023 Elsevier Masson SAS. All rights reserved.