Norm convolution inequalities in Lebesgue spaces

Nursultanov, Erlan; Tikhonov, Sergey; Tleukhanova, Nazerke

doi:10.4171/RMI/1004

Revista Matemática Iberoamericana

Full-Text PDF (362 KB) | Metadata |

Table of Contents |

RMI summary

Volume 34, Issue 2, 2018, pp. 811–838

DOI: 10.4171/RMI/1004

Published online: 2018-05-28

Norm convolution inequalities in Lebesgue spaces

Erlan Nursultanov, Sergey Tikhonov^[1] and Nazerke Tleukhanova

(1) Centre de Recerca Matemática, Bellaterra, Spain, ICREA, Barcelona, Spain, and Universitat Autònoma de Barcelona, Spain

We obtain upper and similar lower estimates of the ($L_p, L_q$) norm for the convolution operator. The upper estimate improves on known convolution inequalities. The technique to obtain lower estimates is applied to study boundedness problems for oscillatory integrals.

Keywords: Convolution, Young–O’Neil inequality, oscillatory kernels

Nursultanov Erlan, Tikhonov Sergey, Tleukhanova Nazerke: Norm convolution inequalities in Lebesgue spaces. Rev. Mat. Iberoam. 34 (2018), 811-838. doi: 10.4171/RMI/1004