T. Absalamov

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Articles: 1

Bisingular Integral with Summable Density

MFAT 31 (2025), no. 3, 153-160

153-160

In this paper, we introduce new metric characteristics in the space of summable functions. Using these metric characteristics it is obtained Zigmund-type inequalities for the bisingular integral. It is constructed an invariant $T_p$ space for bisingular integral operator according to the inequality. Furthermore, the existence and uniqueness of the solution to the nonlinear bisingular integral equation within the invariant space $T_p$ are proven using the method of successive approximations.

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