Multilinear fractional integrals on Morrey spaces

Abstract

In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality.

Olsen-type inequalities for the generalized commutator of multilinear fractional integrals

“…where A i ∈ BMO(R n ). Then we conclude that our results improve [23,Theorem 7.2] and [38,Theorem 1.1].…”

“…where A i ∈ BMO(R n ). Then we conclude that our results improve [23,Theorem 7.2] and [38,Theorem 1.1]. Remark 1.10 As far as we know, Theorem 1.1 is also a new result even if we take m = 1 .…”

“…Moreover, in [38] the authors obtained an Olsen-type inequality for the commutator I b α with a quite elegant method of dyadic decomposition. The reader also can see [23] on an Olsen-type inequality on the multilinear fractional integral I α,m . For more applications of Olsen-type inequalities to PDEs, one may see [14,15,37] for details.…”

Boundedness and Compactness for the Commutators of Bilinear Operators on Morrey Spaces

“…Moreover, the Morrey spaces boundedness of I α was discussed by some authors, see [39,62] and [63], for example. In 2012, Iida et al [40] gave a result, where the range of indexes is sharp.…”

On the Multilinear Singular Integrals and Commutators in the Weighted Amalgam Spaces

“…As is well known, the boundedness of the classical operators in the harmonic analysis on the weighted Morrey spaces has extensively been studied (see [2][3][4][5][6] and references therein). In particular, Wang and Yi [6] recently showed that the -linear commutators and the iterated commutators of the -linear Calderón-Zygmund operators are bounded on weighted Morrey spaces.…”