Fractional integrals on martingale Orlicz-Morrey spaces

Dedicated to Professor Eiichi Nakai on 65th birthday

Abstract

Watari, Chao and Ombe proved the boundedness of the fractional integral I_α, which is a martingale transform, from L_p to L_q 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 I_γ as a martingale transform.