In this paper, we will study the boundedness of a large class of sublinear operators with rough kernel T on the generalized local Morrey spaces LM

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Abstract. Let P be a real n×n matrix, whose all the eigenvalues have positive real part, A t = t P , t > 0 , γ = trP is the homogeneous dimension on R n and Ω is an A t -homogeneous of degree zero function, integrable to a power s > 1 on the unit sphere generated by the corresponding parabolic metric. We study the parabolic fractional maximal and integral operators M P Ω,α and I P Ω,α , 0 < α < γ with rough kernels in the parabolic generalized Morrey space M p,ϕ,P (R n ) . We find conditions on the pair (ϕ 1 ,ϕ 2 ) for the boundedness of the operators M P Ω,α and I PWe also find conditions on ϕ for the validity of the Adams type theoremsMathematics subject classification (2010): 42B20, 42B25, 42B35.