article · Pacific Journal of Mathematics · 1990

Extension theorems for functions of vanishing mean oscillation

Cited by 19Open access

Abstract

A locally integrable function is said to be of vanishing mean oscillation (VMO) if its mean oscillation over cubes in R^ converges to zero with the volume of the cubes. We establish necessary and sufficient conditions for a locally integrable function defined on a bounded measurable set of positive measure to be the restriction to that set of a VMO function.

Cite this paper

APA 7

Holden, P. J. (1990). Extension theorems for functions of vanishing mean oscillation. Pacific Journal of Mathematics, 142(2), 277–295. https://doi.org/10.2140/pjm.1990.142.277

MLA 9

Holden, Peter J. “Extension theorems for functions of vanishing mean oscillation.” Pacific Journal of Mathematics, vol. 142, no. 2, 1990, pp. 277–95, https://doi.org/10.2140/pjm.1990.142.277.

Chicago

Holden, Peter J. 1990. “Extension theorems for functions of vanishing mean oscillation.” Pacific Journal of Mathematics 142 (2): 277–95. https://doi.org/10.2140/pjm.1990.142.277.

Harvard

Holden, P.J. (1990) ‘Extension theorems for functions of vanishing mean oscillation’, Pacific Journal of Mathematics, 142(2), pp. 277–295. Available at: https://doi.org/10.2140/pjm.1990.142.277.

BibTeX

@article{holden1990extension,
  title = {{Extension theorems for functions of vanishing mean oscillation}},
  author = {Holden, Peter J.},
  journal = {Pacific Journal of Mathematics},
  volume = {142},
  number = {2},
  pages = {277--295},
  year = {1990},
  doi = {10.2140/pjm.1990.142.277}
}

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