A Cauchy problem for degenerate parabolic equation of Kolmogorov type of arbitrary order with dependent on only time-variable t coecients is considered. Properties of a volume potential which corresponding to the problem are established in Holder spaces of increased as x→∞" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; color: rgba(0, 0, 0, 0.87); font-family: "Noto Sans", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;">|x|→∞�→∞ functions. From these properties a well-posedness of the Cauchy problem with homogeneous initial conditions is implied.