Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their Applications - Nhan, Nguyen Du Vi; Duc, Dinh Thanh; Tuan, Vu Kim (Armenian Journal of Mathematics, 2009)
n this paper we introduce several iterated convolutions and establish weighted $L_p,\ p>1,-$ norm inequalities for them by using the Hölder’s inequality and the transform of integrals. Applications to wave and heat equations, Klein-Gordon equation are also considered. Especially, we will see their applications to inhomogeneous differential equations.