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Revista Matemática Iberoamericana

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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