UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces

Jorge J. Betancor; Alejandro J. Castro; Lourdes Rodríguez-Mesa

doi:10.1007/s00020-014-2202-5

UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces

Jorge J. Betancor, Alejandro J. Castro, Lourdes Rodríguez-Mesa

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If (Formula presented.) is a UMD Banach space we obtain for (Formula presented.)-valued Hardy and BMO spaces equivalent norms involving γ-radonifying operators and square functions. We also establish characterizations of UMD Banach spaces by means of Hardy and BMO-boundedness properties of g-functions associated to Bessel–Poisson semigroup.

Original language	English
Pages (from-to)	319-374
Number of pages	56
Journal	Integral Equations and Operator Theory
Volume	81
Issue number	3
DOIs	https://doi.org/10.1007/s00020-014-2202-5
Publication status	Published - 2015

Keywords

BMO
Bessel operators
Hardy
Square functions
UMD spaces

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-014-2202-5

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T1 - UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces

AU - Betancor, Jorge J.

AU - Castro, Alejandro J.

AU - Rodríguez-Mesa, Lourdes

PY - 2015

Y1 - 2015

N2 - We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If (Formula presented.) is a UMD Banach space we obtain for (Formula presented.)-valued Hardy and BMO spaces equivalent norms involving γ-radonifying operators and square functions. We also establish characterizations of UMD Banach spaces by means of Hardy and BMO-boundedness properties of g-functions associated to Bessel–Poisson semigroup.

AB - We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If (Formula presented.) is a UMD Banach space we obtain for (Formula presented.)-valued Hardy and BMO spaces equivalent norms involving γ-radonifying operators and square functions. We also establish characterizations of UMD Banach spaces by means of Hardy and BMO-boundedness properties of g-functions associated to Bessel–Poisson semigroup.

KW - BMO

KW - Bessel operators

KW - Hardy

KW - Square functions

KW - UMD spaces

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DO - 10.1007/s00020-014-2202-5

M3 - Article

AN - SCOPUS:84925492977

VL - 81

SP - 319

EP - 374

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 3

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