For a fixed function h we deal with a class of convolution transforms $f;{ ightarrow};f;*;h$, where $(f;*;h)(x);=frac{1}{2x};{int_{{R_{+}}^2}}^{e^1{frac{1}{2}}(xfrac{u^2+y^2}{uy}+frac{yu}{x})};f(u)h(y)dudy,;x;in;R_{+}$ as integral operators $L_p(R_{+};xdx); ightarrow;L_r(R_{+};xdx),;p,;r;{geq};1$. The Young type inequality is proved. Boundedness properties are investigated. Certain examples of these operators are considered and inversion formulas in $L_2(R_{+};xdx)$ are obtained.