Abstract
We establish boundedness properties in a two-parametric family of Lebesgue spaces for certain convolution operators related to the Fourier cosine and Kontorovich–Lebedev transformations. Norm estimations in the weighted L p -spaces are obtained. Natural applications to the corresponding class of convolution integral equations are demonstrated. Necessary and sufficient conditions are found for the solvability of these equations in the weighted L2-spaces.
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