Multidimensional fourier transforms on an Amalgam type space

Elijah Liflyand

Research output: Contribution to journalArticlepeer-review


Generalizing the known results on the Fourier transforms on an amalgam type space, we introduce a multidimensional analogue of such a space, a subspace of L1(Rn+): Integrability results for the Fourier transforms are obtained provided that certain derivatives of the transformed function are in that space. As an application, we obtain conditions for the integrability of multiple trigonometric series.

Original languageEnglish
Pages (from-to)63-74
Number of pages12
JournalEurasian Mathematical Journal
Issue number4
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019 The L.N. Gumilyov Eurasian National University.


  • Amalgam space
  • Bounded variation
  • Fourier transform
  • Integrability
  • Trigonometric series
  • Young inequality


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