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In this paper, we give the inequalities in convolutions in weighted Lp(R,ρ) spaces and their important applications to partial differential equations and integral transforms. Mathematics subject classification (2000): 44A35, 35A22, 26D20. Keywordsandphrases: Convolution, inequality,weighted Lp norm,Green function, integral transform, partial differential equations.

On some convolution norm inequalities in weighted L_p(ℝ^n,ρ) spaces and their applications