Asymmetric Hölder Spaces of Sign Sensitive Weighted Integrable Functions

Authors

  • Miguel A. Jiménez-Pozo Facultad de Ciencias Fí­sico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Ave. San Claudio y 18 Sur, C. U. de San Manuel, Puebla, Pue.72570
  • José M. Hernández-Morales Facultad de Ciencias Fí­sico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Ave. San Claudio y 18 Sur, C. U. de San Manuel, Puebla, Pue.72570

DOI:

https://doi.org/10.26713/cma.v3i1.143

Keywords:

Hölder spaces, Lipschitz functions, Sign-sensitive weights, Weighted integrals, 0-equicontinuous set, Equilipschitzian set, Asymmetric norms

Abstract

We consider the space $L( u,v) $ of $2\pi$-periodic real-valued functions which are integrable with respect to a sign sensitive weight ${(u,v)}$. With some necessary hypothesis for this weight, $L( u,v) $ is an asymmetric Banach space. After defining a convenient modulus of smoothness we introduce the corresponding space $\emph{Lip}_{\alpha}(u,v) $ and its subspace $\emph{lip}_{\alpha }( u,v) $ of Hölder (or Lipschitz) functions associated to this modulus. We prove these spaces are asymmetric Banach spaces too and use the result to study approximation problems.

Downloads

Download data is not yet available.
ICATTA - Proceedings

Downloads

CITATION

How to Cite

Jiménez-Pozo, M. A., & Hernández-Morales, J. M. (2012). Asymmetric Hölder Spaces of Sign Sensitive Weighted Integrable Functions. Communications in Mathematics and Applications, 3(1), 39–50. https://doi.org/10.26713/cma.v3i1.143

Issue

Vol. 3 No. 1 (2012)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.