Estimates of analytic functions in Jordan domain

Bernstein-type inequalities for the derivatives of rational functions in $L\_\{p\}$-spaces, $0<p<1$, on Lavrent{’}ev curves

“…These integrals also occurred in [2,6,7]. Thus, for 1/p ∈ N inequality (1.3) fails for all curves S. In the next statement (Lemma 2.3) we give more explicit expressions for the constant c(S, α) in (2.1) and estimate other integrals of similar nature.…”