Bilinear -type Calderon-Zygmund operators and their commutators on product generalized fractional mixed Morrey spaces

The aim of this paper is to investigate the boundedness of the bilinear theta-type Calderon-Zygmund operator and its commutator on the product of generalized fractional mixed Morrey spaces. Under assumption that the positive and increasing functions phi(.) defined on [0, infinity) satisfy doubling conditions, we prove that the bilinear theta-type Calderon-Zygmund operator (T) over tilde (theta) is bounded from the product of generalized fractional mixed Morrey spaces L-(p) over right arrow1,L-eta 1,L-phi(R-n)xL((p) over right arrow2,eta 2,phi)(R-n) into spaces L-(p) over right arrow,L-eta,L-phi(R-n), where (p) over right arrow (1)=(p(11), ... , p(1n)), (p) over right arrow (2)=(p(21), ... , p(2n)), (p) over right arrow = (p(1), ... , p(n)), 1/(p) over right arrow (1) + 1/(p) over right arrow (2) = 1/(p) over right arrow (1) for 1 < <(p)over right arrow>(1),(p) over right arrow (2) < infinity, and eta=eta(1)+eta(2) for 0 <=eta(1),eta(2),eta < n. Furthermore, the boundedness of the commutator (T) over tilde (theta,b1,b2) formed by b(1),b(2) is an element of BMO(R-n) and (T) over tilde (theta) on spaces L-(p) over right arrow,L-eta,L-phi(R-n) is also obtained.