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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.
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) PublishedText
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
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: 2016-06-22Bibliographically approved

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Castro, Alejandro J.
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