A note on multilinear fractional integrals

Abstract

Shi and Tao [6] studied the boundedness of multilinear fractional integrals introduced by Kenig and Stein [3] on product of weighted L p -spaces, and got some results. We give some remarks with respect to their results and correct some mistakes. We also consider another multilinear fractional integral introduced by Grafakos [2] .

Multilinear fractional integrals on Morrey spaces

“…This is motivated by the results due to Lacey and Thiele [6][7][8]. Recently many people are studying these operators from a various points of view [9][10][11][12][13][14].…”

Weighted estimates for bilinear fractional integral operators

“…Iida, Komori‐Furuya and Sato proved the next theorem; see also Bernicot, Maldonado, Moen and Naibo [, Theorem A].…”

“…In the following, we alway assume that 1 < 1 , 2 < ∞. Iida, Komori-Furuya and Sato [7] proved the next theorem; see also Bernicot, Maldonado, Moen and Naibo [1, Theorem A].…”

Generalized higher commutators generated by the multilinear fractional integrals and Lipschitz functions

“…The multilinear fractional integral operators were also investigated by Kenig and Stein [9]. Recently many people have been studying these operators from various points of view [8,13,15,18].…”