In this paper we establish several weighted norm inequalities for derivatives of products of composition and Laplace convolution of functions. Some generalizations including Yamada's and Opial-type inequalities are discussed. As applications we give L p -weighted estimates for solutions of some integral equations. j f 0 ðxÞj 2 dx: ð1:1Þ Opial-type inequalities involving integrals of functions and their derivatives are essential and in fact indispensable in the theory of di¤erential equations. In [12], Yamada considered an elementary integral inequality which extended a norm inequality of Saitoh [11] and yielded some well-known Opial-type inequalities (see [1]).Independently, some results of Saitoh in [11] were also generalized by the authors [8], in which we presented some weighted norm inequalities for a nonlinear transform in di¤erent normed spaces.Recently, the first two authors [4] considered some norm inequalities for derivatives of products of functions which generalize Saitoh's result [10] and provide an e¤ective tool to estimate Fourier sine and Fourier cosine transforms.In this paper, we will obtain weighted norm inequalities for derivatives of products of composition of functions which generalize some results from ([4], [8]), 228 2010 Mathematics Subject Classification. 26D10; 26A46; 46E35; 44A35.