Abstract: | Let G be a finite domain in the complex plane with K-quasicon formal boundary, z
0
be an arbitrary fixed point in G and p>0. Let jp ( z ): = òx0 x f( z) ]2/8 dz\varphi _p \left( z \right): = \int_{x_0 }^x {\left {\phi \left( \zeta \right)} \right]^{2/8} } d\zeta , and let \iintc | jp ( z ) - Px1 (z) |p d0x \iint\limits_c {\left| {\varphi _p \left( z \right) - P_x^1 (z)} \right|^p d0_x } in the class \mathop ?n \mathop \prod \limits_n of all polynomials of degree `(G)]\bar G in case of $p > 2 - \frac{{K^2 + 1}}{{2K^4 }}$p > 2 - \frac{{K^2 + 1}}{{2K^4 }}
. |