title: On some addition to the Hölder inequality. II
metadata.name: dc.contributor.author
metadata.value: Ivanov, Boris F.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-12-27T14:07:56Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-12-27T14:07:56Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ivanov B.F. On some addition to the Hölder inequality. II. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 4, pp. 586–596.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.407
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/8804
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: If 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 the “non-resonance” condition holds (both concepts have been defined
  by the author for functions from Lp(R1), p ∈ (1,+∞]), then
  sup
  a,b2R1
        
  Zb
  a
  mY
  k=1
  [
  k( ) +  
  k( )] d 
        
  6 C
  mY
  k=1
  k
  k +  
  kkL
  pk
  ak
  (R1),
  where constant C > 0 is independent of functions  
  k ∈ Lpk
  ak (R1) and Lpk
  ak (R1) ⊂ Lpk (R1), 1 6 k 6 m
  are specially constructed normed spaces.
  Besides, we give a boundedness condition for integral of product of functions over a subset of R1.
  Refs 3.
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 4(62); Issue 4
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 Hölder inequality. II
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 07-Ivanov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/8804/1/07-Ivanov.pdf
resources.format: Adobe PDF
resources.size: 275,4 kB