Fundamental inequalities for the iterated Fourier-cosine convolution with Gaussian weight and its application

Derived from the results in (Math. Nachr., 283(12):1758-1770, 2010), in this paper, we devoted to studying the boundedness properties for Fourier-cosine convolution weighted by Gaussian functions via Young's type theorem and Saitoh's type inequality. New norm estimations in the weighted space are obtained and application of the corresponding class of convolutions in Fredholm's second kind of integral equation is discussed. The conditions for the solvability of this equation in L₁ space are also found, along with the analysis of an illustrative example, which exemplifies that the present object and method solve cases that are not under the conditions of previously known techniques.