UMD-Valued Square Functions Associated with Bessel Operators in Hardy and BMO Spaces

作者：Betancor Jorge J; Castro Alejandro J; Rodriguez Mesa Lourdes^*

来源：Integral Equations and Operator Theory, 2015, 81(3): 319-374.

DOI：10.1007/s00020-014-2202-5

• Square functions
• Bessel operators
• UMD spaces
• Hardy
• BMO

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 is a UMD Banach space we obtain for -valued Hardy and BMO spaces equivalent norms involving gamma-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.

• 出版日期2015-3