MATHEMATICS

Sharp $L_p$-inequalities for derivatives of Blaschke products on the straight line

T. S. Mardvilko

Belarusian State University, Minsk

Abstract: Extremal problems for the derivatives of Blaschke products in the Lebesgue space on a straight line are solved. The supremum and infimum of the seminorms $||\!\bullet\!||_{L_p(\mathbb{R})}$, $0<p<\infty$, $p\ne 1/s$ from the derivatives of Blaschke products are obtained. Upper and lower inequalities for the higher derivatives of Blaschke products in the Lebesgue space $L_{1/s}(\mathbb{R})$ were obtained by the author earlier.

Keywords: rational functions, Blaschke products, Bernstein type inequality.

UDC: 517.51+517.53

Received: 04.09.2019