The main object of the study is integral equations of the second kind, which arise when constructing a fundamental solution to the Cauchy problem for a degenerate parabolic equation of Kolmogorov type. The equation may also contain degeneration on the initial hyperplane. The coefficients of this equation are bounded in the group of senior members and increasing functions in the group of junior members. The considered classes of kernels of integral equations allow us to preserve the function in the estimate of the resolvent, which is present in the estimates of the kernels and determines the growth of the coefficients of the parabolic equation.

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