JournalsrmiVol. 34, No. 2pp. 811–838

Norm convolution inequalities in Lebesgue spaces

  • Erlan Nursultanov

    Lomonosov Moscow State University, Kazakhstan Branch, Astana, Kazakhstan and RUDN University, Moscow, Russia
  • Sergey Tikhonov

    Centre de Recerca Matemática, Bellaterra, Spain, ICREA, Barcelona, Spain, and Universitat Autònoma de Barcelona, Spain
  • Nazerke Tleukhanova

    Gumilyov Eurasian National University, Astana, Kazakhstan
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Abstract

We obtain upper and similar lower estimates of the (Lp,LqL_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.

Cite this article

Erlan Nursultanov, Sergey Tikhonov, Nazerke Tleukhanova, Norm convolution inequalities in Lebesgue spaces. Rev. Mat. Iberoam. 34 (2018), no. 2, pp. 811–838

DOI 10.4171/RMI/1004