Commutators of parabolic fractional integrals with variable kernels in vanishing generalized variable Morrey spaces

Abstract

We obtain the boundedness of parabolic fractional integral operators T-Omega,T-alpha with variable kernels Omega(., .) belonging to L-infinity(R-n) x L-s(Sn-1), s > n/(n - alpha), and their commutators [b, T-Omega,T-alpha] with BMO functions in variable exponent generalized Morrey spaces M-p(.),M-phi and variable exponent vanishing generalized Money spaces VMp(.),phi. We find the sufficient conditions on the pair (phi, psi) which ensures the boundedness of the operators T-Omega,T-alpha and [b, T-Omega,T-alpha] from M-p(.),M-phi to M-q(.),M-psi and from VMp(.),phi to VMq(.),psi.