title: Complement to the Hölder inequality for multiple integrals. II
metadata.name: dc.contributor.author
metadata.value: Ivanov, Boris F.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-12-27T14:37:13Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-12-27T14:37:13Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ivanov B. F. Complement to the Hölder inequality for multiple integrals. II. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 4, pp. 612–624. https://doi.org/10.21638/spbu01.2022.404 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.404
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/38717
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This article is the second and final part of the author’s work published in the previous
  issue of the journal. The main result of the article is the statement that if for functions γ1 ∈ Lp1 (Rn), . . . , γm ∈ Lpm(Rn), where m   2 and the numbers p1, . . . , pm ∈ (1,+∞]
  are such that 1
  p1
  + . . . + 1
  pm
  < 1 the “non-resonant” condition is fulfilled (the concept
  introduced by the author in the previous work for functions from spaces Lp(Rn), p ∈
  (1,+∞]), then: supa,b∈Rn
       
   
  [a,b]
  m
   
  k=1
  [γk(τ) +Δγk(τ )] dτ
       
    C
  m
   
  k=1
   γk +Δγk 
  L
  pk
  hk
  (Rn), where
  [a, b] — n-dimensional parallelepiped, the constant C > 0 does not depend on functions
  of Δγk ∈ Lpk
  hk
  (Rn) and Lpk
  hk
  (Rn) ⊂ Lpk (Rn), 1   k   m are some specially constructed
  normalized spaces. In addition, in terms of the fulfillment of some non-resonant condition,
  the paper gives a test of a boundedness of the integral from the product of functions when
  integrating over a subset of Rn.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 9 (67); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: resonance
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Hölder inequality
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Fourier transform
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integral inequalities
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Complement to the Hölder inequality for multiple integrals. II
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 612-624.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/38717/1/612-624.pdf
resources.format: Adobe PDF
resources.size: 328,05 kB