title: On some addition to the H¨older inequality. Resonance case. I
metadata.name: dc.contributor.author
metadata.value: Ivanov, Boris F.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-04-26T09:28:18Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-04-26T09:28:18Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ivanov B. F. On some addition to the H¨older inequality. Resonance case. I. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 1, pp. 70–78.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.108
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/9500
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Let m > 2, numbers p1, . . . , pm ∈ (1,+∞] satisfy inequality
  1
  p1
  + . . . +
  1
  pm
  < 1,
  and functions 
  1 ∈ Lp1 (R1), . . . , 
  m ∈ Lpm(R1).We prove that if the set of “resonance points”
  of each of these functions is not empty and so-called “resonance condition” holds as well then
  there are such arbitrary small (low norm) perturbations  
  k ∈ Lpk (R1) that the resonance
  set of function 
  k +  
  k coincides with the resonance set of function 
  k, 1 6 k 6 m but
  
  
  
  
  
  
  
  t
  Z0
  m
  Yk=1
  [
  k(  ) +  
  k(  )] d 
  
  
  
  
   
  L∞(R1)
  = ∞.
  Concepts of “resonance point” and “resonance condition” for functions from the spaces
  Lp(R1), p ∈ (1,+∞] were introduced by the author in his earlier papers.
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 5(63); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: the H¨older inequality
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On some addition to the H¨older inequality. Resonance case. I
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 08-Ivanov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/9500/1/08-Ivanov.pdf
resources.format: Adobe PDF
resources.size: 306,44 kB