A note on weak existence for singular SDEs

Recently Krylov N. V. Krylov, On time inhomogeneous stochastic Itô equations with drift in [Formula: see text, Ukraïn. Mat. Zh. 72 (2020) 1232–1253] established weak existence of solutions to SDEs for integrable drifts in mixed Lebesgue spaces, whose exponents satisfy the condition Formula: see text, thus going below the celebrated Ladyzhenskaya–Prodi–Serrin condition. We present here a variant of such result, whose proof relies on an alternative technique, based on a partial Zvonkin transform; this allows for drifts with growth at infinity and/or in uniformly local Lebesgue spaces.