Watari, Chao and Ombe proved the boundedness of the fractional integral Iα, which is a martingale transform, from Lp to Lq for 1 < p < q < ∞, 0 < α < 1 and −1/p+α = −1/q. This boundedness was also extended to martingale Orlicz and Morrey spaces by Arai et al. and Nakai and Sadasue, respectively. In this paper, we extend these boundedness to martingale Orlicz-Morrey spaces by using the generalized fractional integral Iγ as a martingale transform.
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