Boundedness of Convolution and Polyconvolution Operators Associated With Hartley‐Fourier Cosine on Dual Spaces With Applications

ABSTRACT The Hausdorff–Young inequality is recognized as one of the fundamental results in the theory of Fourier analysis. Establishing Hausdorff–Young type inequalities for convolution and polyconvolution operators constitutes a natural and significant extension of this classical viewpoint. In this paper, we contribute to this line of research by constructing a new Hausdorff–Young type inequality for the Hartley convolution and the cosine Hartley–Fourier polyconvolution operators. As a direct consequence, the boundedness of these operators on dual spaces is obtained. Furthermore, several illustrative examples are provided to demonstrate the solvability and boundedness of explicit solutions for certain classes of integral and differential equations, thereby offering a comprehensive perspective on both the theoretical and applied aspects of these extended inequalities.