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In this paper, some elementary and useful terminologies associated to Lebedev–Skalskaya transform (LS-transform) are notified and then estimates for R κ 1 2 + i τ (x) , F κ 1 2 + i τ (x) , translation and convolution operators associated to LS-transform are obtained. The continuity of LS-transforms, translation and convolution operators on functions spaces S α , k , H α , k and G α , k are discussed. The continuity of pseudo-differential operators in terms of LS-transforms is discussed on functions spaces S α , k , H α , k , G α , k and Lebesgue space. At the end, an application of LS-transform is shown by solving a differential equation of convolution type. [ABSTRACT FROM AUTHOR]