## Abstract

TA direct theorem for best polynomial approximation of a function in L_{p},0< p< 1 has recently been established. Here we present a matching inverse theorem. In particular, we obtain as a corollary the equivalence for 0 < α < k between The present result complements the known direct and inverse theorem for best polynomial approximation in Analogous results for approximating periodic functions by trigonometric polynomials in L_{p}[π, π] 0 < p ≤ ∞ are known.

Original language | English |
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Pages (from-to) | 151-155 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 120 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1994 |

## Keywords

- 0 < p < 1
- Best polynomial approximation
- Inverse theorems
- L spaces

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