Calderón-Zygmund operators in the Bessel setting for all possible type indices

被引：0
作者：
Alejandro J. Castro
Tomasz Z. Szarek
机构：
[1] Universidad de La Laguna,Departamento de Análisis Matemático
[2] Polska Akademia Nauk,Instytut Matematyczny
来源：
Acta Mathematica Sinica, English Series | 2014年 / 30卷
关键词：
Bessel operator; Bessel semigroup; maximal operator; square function; multiplier; Riesz transform; Calderón-Zygmund operator; 42C05; 42B20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-Paley-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as, Calderón-Zygmund operators for all possible values of type parameter λ in this context. This extends results existing in the literature, but being justified only for a restricted range of λ.
引用
收藏
页码：637 / 648
页数：11
相关论文
共 45 条
[1]  
Andersen K F(1975)Norm inequalities for ultraspherical and Hankel conjugate functions Canad. J. Math. 27 162-171
[2]  
Andersen K F(1981)Weighted norm inequalities for generalized Hankel conjugate transformations Studia Math. 71 15-26
[3]  
Kerman R A(2007)Riesz transforms related to Bessel operators Proc. Roy. Soc. Edinburgh Sect. A 137 701-725
[4]  
Betancor J J(2011)Spectral multipliers for multidimensional Bessel operators J. Fourier Anal. Appl. 17 932-975
[5]  
Buraczewski D(2012)Harmonic analysis operators associated with multidimensional Bessel operators Proc. Roy. Soc. Edinburgh Sect. A 142 945-974
[6]  
Fariña J C(2014)Weak type (1, 1) estimates for Caffarelli-Calderón generalized maximal operators for semigroups associated with Bessel and Laguerre operators Proc. Amer. Math. Soc. 142 251-261
[7]  
Betancor J J(2012)Calderón-Zygmund operators in the Bessel setting Monatsh. Math. 167 375-403
[8]  
Castro A J(2008)Higher order Riesz transforms associated with Bessel operators Ark. Mat. 46 219-250
[9]  
Curbelo J(2009)On Littlewood-Paley functions associated with Bessel operators Glasg. Math. J. 51 55-70
[10]  
Betancor J J(2010)Mapping properties of fundamental operators in harmonic analysis related to Bessel operators Studia Math. 197 101-140
12345