In this paper, some elementary and useful terminologies associated to Lebedev–Skalskaya transform (LS-transform) are notified and then estimates for $\mathfrak{R}{\kappa }_{\frac{1}{2}+i\tau }(x)$, $\mathfrak{F}{\kappa }_{\frac{1}{2}+i\tau }(x)$, translation and convolution operators associated to LS-transform are obtained. The continuity of LS-transforms, translation and convolution operators on functions spaces ${\mathfrak{S}}^{\alpha ,k}$, ${\mathcal{H}}^{\alpha ,k}$ and ${\mathcal{G}}^{\alpha ,k}$ are discussed. The continuity of pseudo-differential operators in terms of LS-transforms is discussed on functions spaces ${\mathfrak{S}}^{\alpha ,k}$, ${\mathcal{H}}^{\alpha ,k}$, ${\mathcal{G}}^{\alpha ,k}$ and Lebesgue space. At the end, an application of LS-transform is shown by solving a differential equation of convolution type.

在本文中，通知了与 Lebedev-Skalskaya 变换 (LS-transform) 相关的一些基本且有用的术语，然后估计$\mathfrak{R}{\kappa }_{\frac{1}{2}+\mathrm{一世}\tau }(X)$,$\mathfrak{F}{\kappa }_{\frac{1}{2}+\mathrm{一世}\tau }(X)$，获得与LS变换相关的平移和卷积算子。函数空间上 LS 变换、平移和卷积算子的连续性${\mathfrak{小号}}^{\alpha ,ķ}$,${\mathcal{H}}^{\alpha ,ķ}$和${\mathcal{G}}^{\alpha ,ķ}$被讨论。在函数空间上讨论了伪微分算子在 LS 变换方面的连续性${\mathfrak{小号}}^{\alpha ,ķ}$,${\mathcal{H}}^{\alpha ,ķ}$,${\mathcal{G}}^{\alpha ,ķ}$和勒贝格空间。最后，通过求解卷积类型的微分方程展示了LS变换的应用。