title: On some addition to the H¨older inequality. Resonance case. II
metadata.name: dc.contributor.author
metadata.value: Ivanov, Boris F.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-07-12T19:31:58Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-07-12T19:31:58Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ivanov B. F. On some addition to the H¨older inequality. Resonance case. II. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 2, pp. 233–243.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.204
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/10401
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Let m > 2, numbers p1, . . . , pm 2 (1,+1] satisfy inequality
  1
  p1
  + . . . +
  1
  pm
  < 1,
  and functions 
  1 2 Lp1 (R1), . . . , 
  m 2 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
  too then there exist such arbitrary small (low norm) perturbations  
  k 2 Lpk (R1) that the
  resonance set of the function 
  k + 
  k coincides with the resonance set of the function 
  k,
  1 6 k 6 m, but at the same time
  
  
  
  
  
  
  
  t
  Z
  0
  m
  Yk=1
  [
  k(  ) +  
  k(  )] d 
  
  
  
  
   
  L∞(R1)
  = 1.
  Concepts of a “resonance point” and of a “resonance condition” for functions from the spaces
  Lp(R1), p 2 (1,+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 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: H¨older inequality
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On some addition to the H¨older inequality. Resonance case. II
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 04-Ivanov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/10401/1/04-Ivanov.pdf
resources.format: Adobe PDF
resources.size: 315,33 kB