title: Complement to the Hlder inequality for multiple integrals. I
metadata.name: dc.contributor.author
metadata.value: Ivanov, Boris F.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-07-07T21:31:10Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-07-07T21:31:10Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ivanov B. F. Complement to the Hölder inequality for multiple integrals. I. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 2, pp. 255–268.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.207
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/37105
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This article is the first part of the work, the main result of which 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, a non-resonant condition is met (the concept introduced by the author for functions from 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]
  is an n-dimensional parallelepiped, the constant C > 0 does not depend on functions
  Δγk ∈ Lpk
  hk
  (Rn), and Lpk
  hk
  (Rn) ⊂ Lpk (Rn), 1   k   m, are specially constructed normalized
  spaces. In the article, for any spaces Lp0 (Rn), Lp(Rn), p0, p ∈ (1,+∞] and any function
  γ ∈ Lp0 (Rn) the concept of a set of resonant points of a function γ with respect to the
  Lp(Rn) is introduced. This set is a subset of {R1 ∪{∞}}n for any trigonometric polynomial
  of n variables with respect to any Lp(Rn) represents the spectrum of the polynomial in
  question. Theorems are written on the representation of each function γ ∈ Lp0 (Rn) with a
  nonempty resonant set as the sum of two functions such that the first of them belongs to
  the Lp0 (Rn) ∩ Lq(Rn), 1
  p + 1
  q = 1, and the carrier of the Fourier transform of the second is
  centered in the neighborhood of the resonant set.
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 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: the Hölder inequality
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Complement to the Hlder inequality for multiple integrals. I
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 255-268.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/37105/1/255-268.pdf
resources.format: Adobe PDF
resources.size: 349,48 kB