uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Square Functions And Spectral Multipliers For Bessel Operators In Umd Spaces
Univ La Laguna, Dept Anal Matemat, Campus Anchieta, San Cristobal la Laguna 38271, Sta Cruz De Ten, Spain..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Univ La Laguna, Dept Anal Matemat, Campus Anchieta, San Cristobal la Laguna 38271, Sta Cruz De Ten, Spain..
2016 (English)In: Banach Journal of Mathematical Analysis, ISSN 1735-8787, Vol. 10, no 2, 338-384 p.Article in journal (Refereed) Published
Resource type
Text
Abstract [en]

In this paper, we consider square functions (also called Littlewood-Paley g-functions) associated to Hankel convolutions acting on functions in the Bochner Lebesgue space L-p((0, infinity), B), where B is a UMD Banach space. As special cases, we study square functions defined by fractional derivatives of the Poisson semigroup for the Bessel operator Delta(lambda) = -x(-lambda) d/dxx(2 lambda)d/dxx(-lambda), lambda > 0. We characterize the UMD property for a Banach space I; by using L-p((0, infinity), B)-boundedness properties of g-functions defined by Bessel Poisson semigroups. As a by-product, we prove that the fact that the imaginary power Delta(iw)(lambda), w is an element of R \ {0}, of the Bessel operator Delta(lambda) is bounded in L-p((0, infinity), In), 1 < p < infinity, characterizes the UMD property for the Banach space B. As applications of our results for square functions, we establish the boundedness in L-p((0, infinity), B) of spectral multipliers m(Delta(lambda)) of Bessel operators defined by functions m which are holomorphic in sectors Sigma(v).

Place, publisher, year, edition, pages
2016. Vol. 10, no 2, 338-384 p.
Keyword [en]
UMD space, square function, spectral multiplier, Bessel operator, gamma-radonifying operator
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-297128DOI: 10.1215/17358787-3495627ISI: 000374785700008OAI: oai:DiVA.org:uu-297128DiVA: diva2:941124
Available from: 2016-06-22 Created: 2016-06-21 Last updated: 2017-02-21Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Castro, Alejandro J.
By organisation
Analysis and Probability Theory
In the same journal
Banach Journal of Mathematical Analysis
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 199 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf