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The aim of this paper is to give Adams-Spanne type estimates for parabolicsublinear operators and their commutators by with rough kernels generated byparabolic fractional integral operators under generic size conditions which aresatisfied by most of the operators in harmonic analysis. Their endpointestimates are also disposed.

Adams-Spanne type estimates for parabolic sublinear operators and their commutators by with rough kernels on parabolic generalized Morrey spaces