Boundedness In Weighted L-P Spaces For The Kontorovich-Lebedev-Fourier Generalized Convolutions And Applications

In this paper several weighted -norm inequalities (p>1) for the Kontorovich-Lebedev-Fourier generalized convolutions are obtained. With the help of these inequalities we consider a parabolic integro-differential equation of second order and study the boundedness of its solution in weighted spaces. Moreover, the boundedness of a scattered acoustic field in weighted spaces is also obtained.