Bernstein’s Inequality for the Weyl Derivatives of Trigonometric Polynomials in the Space L0

详细

A logarithmic asymptotics for the behavior with respect to n of the exact constant in Bernstein’s inequality for the Weyl derivative of positive noninteger order of trigonometric polynomials of order n in the space L₀ is obtained. It turns out that the order in n of the behavior of this constant for positive noninteger orders of the derivatives has exponential growth in contrast to the power growth in the well-studied case of classical derivatives of positive integer order.