A Note on VLO Functions

Francesca Angrisani; Giacomo Ascione

Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche (2018)

  • Volume: 85, Issue: 1, page 177-183
  • ISSN: 0370-3568

Abstract

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Inspired by a result from Leibov, we find that the supremum defining the B ⁢ L ⁢ O norm in [ 0 , 1 ] is actually attained by a specific sub-interval of [ 0 , 1 ] for f ∈ V ⁢ L ⁢ O ⁢ ( [ 0 , 1 ] )

How to cite

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Angrisani, Francesca, and Ascione, Giacomo. "A Note on VLO Functions." Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche 85.1 (2018): 177-183. <http://eudml.org/doc/296739>.

@article{Angrisani2018,
abstract = {Inspired by a result from Leibov, we find that the supremum defining the $BLO$ norm in $[0, 1]$ is actually attained by a specific sub-interval of $[0, 1]$ for $f \in VLO([0, 1])$},
author = {Angrisani, Francesca, Ascione, Giacomo},
journal = {Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche},
keywords = {BLO; VLO; norm-attaining},
language = {eng},
month = {12},
number = {1},
pages = {177-183},
publisher = {Società Nazione di Scienze, Lettere e Arti in Napoli; Giannini},
title = {A Note on VLO Functions},
url = {http://eudml.org/doc/296739},
volume = {85},
year = {2018},
}

TY - JOUR
AU - Angrisani, Francesca
AU - Ascione, Giacomo
TI - A Note on VLO Functions
JO - Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche
DA - 2018/12//
PB - Società Nazione di Scienze, Lettere e Arti in Napoli; Giannini
VL - 85
IS - 1
SP - 177
EP - 183
AB - Inspired by a result from Leibov, we find that the supremum defining the $BLO$ norm in $[0, 1]$ is actually attained by a specific sub-interval of $[0, 1]$ for $f \in VLO([0, 1])$
LA - eng
KW - BLO; VLO; norm-attaining
UR - http://eudml.org/doc/296739
ER -

References

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  1. Angrisani, F. (2017), On the distance in B ⁢ L ⁢ O ⁢ ( ℝ ) to L ∞ ⁢ ( ℝ ) and V ⁢ L ⁢ O ⁢ ( ℝ ) , Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche di Napoli, 4.84, 75-86. 
  2. Coifman, R. R. and Rochberg, R. (1980), Another characterization of B ⁢ M ⁢ O , Proceedings of the American Mathematical Society, 249-254. Zbl0432.42016MR565349DOI10.2307/2043245
  3. John, F. and Nirenberg, L. (1961), On functions of bounded mean oscillation, Communications on pure and applied Mathematics, 14.3, 415-426. Zbl0102.04302MR131498DOI10.1002/cpa.3160140317
  4. Korey, M. B. (2001), A decomposition of functions with vanishing mean oscillation, Harmonic Analysis and Boundary Value Problems: Selected Papers from the 25th University of Arkansas Spring Lecture Series, Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View, March 2-4, 2000, Fayetteville, Arkansas, 277, 45. 
  5. Leibov, M. V. (1990), Subspaces of the V ⁢ M ⁢ O space, Journal of Soviet Mathematics, 48.5, 536-538. Zbl0711.42028MR865789DOI10.1007/BF01095622
  6. Sarason, D. (1975), Functions of vanishing mean oscillation, Transactions of the American Mathematical Society, 207, 391-405. Zbl0319.42006MR377518DOI10.2307/1997184

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