**Abstract**

In the present manuscript, we prove that the singular numbers of the Cauchy transform <sup>L</sup>*σ*½ � *<sup>f</sup>* ð Þ¼� *<sup>z</sup>* <sup>1</sup> *π* Ð *f*ð Þ*ξ <sup>ξ</sup>*�*<sup>z</sup> log* <sup>1</sup> ∣*z*�*ξ*∣ � � <sup>1</sup> � *ξξ* � �*<sup>σ</sup>*�<sup>2</sup> *dμ ξ*ð Þ (2) defined on the space *<sup>L</sup>*2,*<sup>σ</sup>*ð Þ of complex-valued measurable functions, which are 1 � *ξξ* � �*<sup>σ</sup>*�<sup>2</sup> *dμ ξ*ð Þ-square integrable on where *σ* >1 is a fixed parameter, are asymptotically ≈*C* ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *<sup>k</sup><sup>m</sup>*�4*ν*þ<sup>1</sup> <sup>p</sup> , as *k* ! ∞ where *C* is a constant.

**Keywords:** the logarithmic potential transform, the singular values, Cauchy transform.
