title: On some addition to the Hölder inequality. I
metadata.name: dc.contributor.author
metadata.value: Ivanov, Boris F.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-09-20T13:40:30Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-09-20T13:40:30Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ivanov B. F. On some addition to the Hölder inequality. I. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 3, pp. 436–447.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.306
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/7146
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 the “non-resonance” condition holds (both concepts have been defined
  by the author for functions from Lp(R1), p ∈ (1,+∞]), then
  sup
  a,b2R1
        
  b
  Z
  a
  m
  Yk=1
  [
  k( ) +  
  k( )] d       
  6 C
  m
  Yk=1
  k
  k +  
  kkL
  pk
  ak
  (R1),
  where constant C > 0 is independent on functions  
  k ∈ L
  pk
  ak (R1) and L
  pk
  ak (R1) ⊂ Lpk (R1), 1 6 k 6 m
  are specially constructed normed spaces.
  Besides, we give a condition of integral boundedness from the product of functions when integrating
  over a subset of R1. Refs 12.
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 3
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. I
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 06-Ivanov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/7146/1/06-Ivanov.pdf
resources.format: Adobe PDF
resources.size: 293,08 kB