Boundedness of multilinear operators on generalized Morrey spaces

Multilinear BMO Estimates for the Commutators of Multilinear Fractional Maximal and Integral Operators on the Product Generalized Morrey Spaces

“…by Moen [20] and Chen-Xue [3], respectively. Yu and Tao [29] have also obtained the boundedness of the operators I…”

Multilinear BMO estimates for the commutators of multilinear fractional maximal and integral operators on the product generalized Morrey spaces

“…Here, 1 < p < ∞ and 0 < λ < n and the quantity of (1.1) is the (p, λ)-Morrey norm, denoted by f L p,λ . In recent years, more and more researches focus on function spaces based on Morrey spaces to fill in some gaps in the theory of Morrey type spaces (see, for example, [10,12,13,14,15,16,18,20,26,28,32]). Moreover, these spaces are useful in harmonic analysis and PDEs.…”

“…Later, weighted inequalities for the multilinear fractional integral operators have been established by Moen [23] and Chen-Xue [3], respectively. Yu and Tao [32] have also obtained the boundedness of the operators I (m) α , T (m) and M (m) (m ∈ N) on the product generalized Morrey spaces, respectively. Indeed their results (Theorem 2.1., Theorem 3.1. and Theorem 4.1. in [32]) are the extensions of Theorem 4.5., Corollary 4.6., Theorem 5.4. and Corollary 5.5. in [11].…”

Multi-sublinear operators and their commutators on product generalized mixed Morrey spaces

“…We first prove the Guliyev local estimate (see, for example, [11,14] in the case m = 1 and [13,16,29] in the case m > 1), which gives us an explicit estimate for the L q (R n ) norm of T m on a given ball B(x 0 , r). Here and in what follows, we use the notation q = (q 1 , • • • , q n ) and…”