In this paper, we obtain the inequalities for the iterated convolution and their applications to physical problems. We also get the inequalityand its applications in L p (R n , |ρ|) space. (2000): 44A35, 35A22, 26D20. Mathematics subject classification

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Abstract. In this paper, we give some new type of convolution inequalities in weighted L p (R 2 , dxdy) spaces and their important applications to partial differential equations and integral transforms. Especially, we will see their applications to non-homogeneous linear differential equations.

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