Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T04:18:57.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Orlicz–Besov Extension and Imbedding

Part of: Harmonic analysis in several variables Linear function spaces and their duals

Published online by Cambridge University Press:  01 July 2019

Hongyan Sun
Hongyan Sun*
Affiliation:
Department of Sciences, China University of Geosciences, Beijing100083, P.R. China Email: sun_hy@cugb.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

We establish criteria for Orlicz–Besov extension/imbedding domains via (global) $n$-regular domains that generalize the known criteria for Besov extension/imbedding domains.

Keywords

Orlicz–Besov extensionOrlicz–Besov imbbeding(global) n-regular domain

MSC classification

Primary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Secondary: 42B35: Function spaces arising in harmonic analysis
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 1 , March 2020 , pp. 222 - 241
Copyright
© Canadian Mathematical Society 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The author was supported by the National Natural Science of Foundation of China (No. 11601494).

References

Adams, R. A. and Fournier, J. J. F., Sobolev spaces. Elsevier/Academic Press, Amsterdam, 2003.Google Scholar
DeVore, R. A. and Sharpley, R. C., Besov spaces on domains in R d. Trans. Amer. Math. Soc. 335(1993), 843–864.Google Scholar
Grafakos, L., Classical and modern fourior analysis. Pearson Education, Upper Saddle River, NJ, 2004.Google Scholar
Gogatishvili, A., Koskela, P., and Zhou, Y., Characterizations of Besov and Triebel-Lizorkin spaces on metric measure spaces. Forum Math. 25(2013), 787–819. https://doi.org/10.1515/form.2011.135Google Scholar
Hajłasz, P., Koskela, P., and Tuominen, H., Sobolev imbeddings, extensions and measure density condition. J. Funct. Anal. 254(2008), 1217–1234. https://doi.org/10.1016/j.jfa.2007.11.020Google Scholar
Hajłasz, P., Koskela, P., and Tuominen, H., Measure density and extendability of Sobolev functions. Rev. Mat. Iberoam. 24(2008), 645–669.Google Scholar
Jones, P. W., Extension theorems for BMO. Indiana Univ. Math. J. 29(1980), 41–66.Google Scholar
Jones, P. W., Quasiconformal mappings and extendability of functions in Sobolev spaces. Acta Math. 147(1981), 71–88.Google Scholar
Jonsson, A. and Wallin, H., A Whitney extension theorem in L p and Besov spaces. Ann. Inst. Fourier (Grenoble) 28(1978), 139–192.Google Scholar
Jonsson, A. and Wallin, H., Function spaces on subsets of ℝn. Math. Rep. 2(1984), no. 1.Google Scholar
Koskela, P., Extensions and imbeddings. J. Funct. Anal. 159(1998), 369–384. https://doi.org/10.1006/jfan.1998.3331Google Scholar
Koskela, P., Zhang, Y., and Zhou, Y., Morrey-Sobolev extension domains. J. Geom. Anal. 27(2017), 1413–1434. https://doi.org/10.1007/s12220-016-9724-9Google Scholar
Liang, T. and Zhou, Y., Orlicz-Besov extension and Ahlfors n-regular domains. arxiv:1901.06186Google Scholar
Piaggio, M. C., Orlicz spaces and the large scale geometry of Heintze groups. Math. Ann. 368(2017), 433–481. https://doi.org/10.1007/s00208-016-1430-1Google Scholar
Rychkov, V. S., On restrictions and extensions of the Besov and Triebel-Lizorkin spaces with respect to Lipschitz domains. J. London Math. Soc. (2) 60(1999), 237–257. https://doi.org/10.1112/S0024610799007723Google Scholar
Shvartsman, P., Local approximations and intrinsic characterizations of spaces of smooth functions on regular subsets of ℝn. Math. Nachr. 279(2006), 1212–1241. https://doi.org/10.1002/mana.200510418Google Scholar
Shvartsman, P., On extensions of Sobolev functions defined on regular subsets of metric measure spaces. J. Approx Theory 144(2007), 139–161.Google Scholar
Shvartsman, P., On Sobolev extension domains in R n. J. Funct. Anal. 258(2010), 2205–2245. https://doi.org/10.1016/j.jfa.2010.01.002Google Scholar
Sun, H., Orlicz-Besov imbedding and globally n-regular domains. arxiv:1810.03796Google Scholar
Stein, E. M., Singular integrals and differentiability properties of functions. Princeton Mathematical Series, 30, Princeton University Press, Princeton, NJ, 1970.Google Scholar
Triebel, H., Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers. Rev. Mat. Complut. 15(2002), 475–524. https://doi.org/10.5209/rev_REMA.2002.v15.n2.16910Google Scholar
Triebel, H., Function spaces and wavelets on domains. EMS Tracts in Mathematics, 7, European Mathematical Society, Zürich, 2008.Google Scholar
Wang, Z., Xiao, J., and Zhou, Y., Q 𝛼-extension and Ahlfors n-regular domains. Asian. J. Math.(2019), to appear.Google Scholar
Zhou, Y., Fractional Sobolev extension and imbedding. Trans. Amer. Math. Soc. 367(2015), 959–979. https://doi.org/10.1090/S0002-9947-2014-06088-1Google Scholar