Speaker
Dmitry Gorbachev
(Tula State University)
Description
Bernstein's inequality for the derivative of a trigonometric polynomial in the $L^p$ space is a classical inequality of approximation theory. It has been generalized to the case of entire functions of exponential type on the axis. The question of
boundedness of the constant remained open in the case of a power weight for $p > 0$. We show that this is true for both the ordinary derivative and the Dunkl differential-difference operator.
