On Bernstein–Walsh-type lemmas in regions of the complex plane

Polynomial inequalities in Lavrentiev regions with interior and exterior zero angles in the weighted Lebesgue space

“…Results analogous to (1.2) for some different norms and unbounded regions were obtained in [22], [2][3][4][5][6][7] and others.…”

On some inequalities for derivatives of algebraic polynomials in unbounded regions with angles

“…was found in [3] (see, also [2]), where 𝑅 * : = 1 + 𝑐 2 (𝑅 − 1), 𝑐 2 > 0 and 𝑐 1 : = 𝑐 1 (𝐺, 𝑝, 𝑐 2 ) > 0 constants, independent from 𝑛 and 𝑅. It's well known that quasiconformal curves can be non-rectifiable (see, for example, [16], [20, p.104] ) ,…”

“…Some auxiliary resultsLemma 1 [1]. Let 𝐿 be a 𝐾 −quasiconformal curve, 𝑧 1 ∈ 𝐿, 𝑧 2 , 𝑧3 ∈ 𝛺 ∩ {𝑧: |𝑧 − 𝑧 1 | ≺ 𝑑(𝑧 1 , 𝐿 𝑅 0 )}; 𝑤 𝑗 = 𝛷(𝑧 𝑗 ), (𝑧 2 , 𝑧 3 ∈ 𝐺 ∩ {𝑧: |𝑧 − 𝑧 1 | ≺ 𝑑(𝑧 1 , 𝐿 𝑅 0 )}; 𝑤 𝑗 = 𝜑(𝑧 𝑗 )), 𝑗 = 1,2,3. Then a) The statements |z 1 − z 2 | ≺ |z 1 − z 3 | and |w 1 − w 2 | ≺ |w 1 − w 3 | are equivalent.…”