### Abstract

In this paper, we give L ^{p} - L ^{q} estimates and the L ^{F} regularizing estimate of Radon transforms associated to real analytic functions, and we also give estimates of the decay rate of the L ^{p} operator norm of corresponding oscillatory integral operators. For L ^{p} - L ^{q} estimates and estimates of the decay rate of the L ^{p} operator norm we obtain sharp results except for extreme points; however, for L ^{p} regularity we allow some restrictions on the phase function.

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

Pages (from-to) | 3887-3903 |

Number of pages | 17 |

Journal | Transactions of the American Mathematical Society |

Volume | 357 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2005 Oct 1 |

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### Keywords

- Oscillatory integral operator
- Radon transform

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**L ^{p} improving estimates for some classes of Radon transforms.** / Yang, Chan Woo.

Research output: Contribution to journal › Article

^{p}improving estimates for some classes of Radon transforms',

*Transactions of the American Mathematical Society*, vol. 357, no. 10, pp. 3887-3903. https://doi.org/10.1090/S0002-9947-05-03807-9

}

TY - JOUR

T1 - L p improving estimates for some classes of Radon transforms

AU - Yang, Chan Woo

PY - 2005/10/1

Y1 - 2005/10/1

N2 - In this paper, we give L p - L q estimates and the L F regularizing estimate of Radon transforms associated to real analytic functions, and we also give estimates of the decay rate of the L p operator norm of corresponding oscillatory integral operators. For L p - L q estimates and estimates of the decay rate of the L p operator norm we obtain sharp results except for extreme points; however, for L p regularity we allow some restrictions on the phase function.

AB - In this paper, we give L p - L q estimates and the L F regularizing estimate of Radon transforms associated to real analytic functions, and we also give estimates of the decay rate of the L p operator norm of corresponding oscillatory integral operators. For L p - L q estimates and estimates of the decay rate of the L p operator norm we obtain sharp results except for extreme points; however, for L p regularity we allow some restrictions on the phase function.

KW - Oscillatory integral operator

KW - Radon transform

UR - http://www.scopus.com/inward/record.url?scp=26444477006&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26444477006&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-05-03807-9

DO - 10.1090/S0002-9947-05-03807-9

M3 - Article

AN - SCOPUS:26444477006

VL - 357

SP - 3887

EP - 3903

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 10

ER -