### Abstract

Let G be a compact abelian group and r its dual. For 1 ≤ q > ∞, the space Aq(G) is defined as with the norm We prove: Let G be a compact, connected abelian group and P any fixed order on Γ. If q <2 and Φi s a Young’s function, then the conjugation operator H does not extend to a bounded operator from Aq(G) to the Orlicz space L^{Φ}.

Original language | English |
---|---|

Pages (from-to) | 163-166 |

Number of pages | 4 |

Journal | Proceedings of the American Mathematical Society |

Volume | 121 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1994 |

### Fingerprint

### Keywords

- Conjugation operator
- Rudin-Shapiro polynomials

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

_{q}(G).

*Proceedings of the American Mathematical Society*,

*121*(1), 163-166. https://doi.org/10.1090/S0002-9939-1994-1181167-4

**The conjugation operator on A _{q}(G).** / Gupta, Sanjiv Kumar; Madan, Shobha; Tewari, U. B.

Research output: Contribution to journal › Article

_{q}(G)',

*Proceedings of the American Mathematical Society*, vol. 121, no. 1, pp. 163-166. https://doi.org/10.1090/S0002-9939-1994-1181167-4

_{q}(G). Proceedings of the American Mathematical Society. 1994;121(1):163-166. https://doi.org/10.1090/S0002-9939-1994-1181167-4

}

TY - JOUR

T1 - The conjugation operator on Aq(G)

AU - Gupta, Sanjiv Kumar

AU - Madan, Shobha

AU - Tewari, U. B.

PY - 1994

Y1 - 1994

N2 - Let G be a compact abelian group and r its dual. For 1 ≤ q > ∞, the space Aq(G) is defined as with the norm We prove: Let G be a compact, connected abelian group and P any fixed order on Γ. If q <2 and Φi s a Young’s function, then the conjugation operator H does not extend to a bounded operator from Aq(G) to the Orlicz space LΦ.

AB - Let G be a compact abelian group and r its dual. For 1 ≤ q > ∞, the space Aq(G) is defined as with the norm We prove: Let G be a compact, connected abelian group and P any fixed order on Γ. If q <2 and Φi s a Young’s function, then the conjugation operator H does not extend to a bounded operator from Aq(G) to the Orlicz space LΦ.

KW - Conjugation operator

KW - Rudin-Shapiro polynomials

UR - http://www.scopus.com/inward/record.url?scp=84966257178&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966257178&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1994-1181167-4

DO - 10.1090/S0002-9939-1994-1181167-4

M3 - Article

VL - 121

SP - 163

EP - 166

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -