**Larry Gogoladze**

## On the Convergence of Conjugate
Trigonometric Polynomials

**Abstract:**

Sufficient conditions are found, under which for $f\in C([-\pi,\pi])$ or $f\in
L([-\pi,\pi])$ the convergence of a sequence of trigonometric polynomials in the
norms of these spaces implies the convergence of their conjugates in the same
norms.

**Keywords:**

Conjugate functions, de la Vallée-Poussin
means, best approximation.

**MSC 2000:** 42A50