Dimension free Lp estimates for single Riesz transforms via an H∞ joint functional calculus

被引:8
作者
Wrobel, Blazej [1 ,2 ]
机构
[1] Uniwersytet Wroclawski, Inst Matemat, PL-50384 Wroclaw, Poland
[2] Scuola Normale Super Pisa, I-56126 Pisa, Italy
关键词
Riesz transforms; Dimension free L-p estimates; H-infinity joint functional calculus; LAGUERRE FUNCTION EXPANSIONS; HARMONIC-ANALYSIS; RANDOM-WALKS; CONJUGACY; OPERATORS;
D O I
10.1016/j.jfa.2014.07.005
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
By using an H-infinity joint functional calculus for strongly commuting operators, we derive a scheme to deduce the L-p boundedness of certain d-dimensional Riesz transforms from the L-p boundedness of appropriate one-dimensional Riesz transforms. Moreover, the L-p bounds we obtain are independent of the dimension. The scheme is applied to Riesz transforms connected with orthogonal expansions and discrete Riesz transforms on products of groups with polynomial growth. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:3332 / 3350
页数:19
相关论文
共 48 条
[1]   Holomorphic functional calculi and sums of commuting operators [J].
Albrecht, D ;
Franks, E ;
McIntosh, A .
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1998, 58 (02) :291-305
[2]  
Alexopoulos GK, 2002, ANN PROBAB, V30, P723
[3]  
[Anonymous], 2012, GRAD TEXTS MATH
[4]  
[Anonymous], LINEAR DIMENSION FRE
[5]   INTERPOLATION OF SOBOLEV SPACES, LITTLEWOOD-PALEY INEQUALITIES AND RIESZ TRANSFORMS ON GRAPHS [J].
Badr, Nadine ;
Russ, Emmanuel .
PUBLICACIONS MATEMATIQUES, 2009, 53 (02) :273-328
[6]  
BAKRY D, 1987, LECT NOTES MATH, V1247, P137
[7]   Harmonic analysis operators associated with multidimensional Bessel operators [J].
Betancor, Jorge J. ;
Castro, Alejandro J. ;
Curbelo, Jezabel .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2012, 142 (05) :945-974
[8]   ON SINGULAR INTEGRALS [J].
CALDERON, AP ;
ZYGMUND, A .
AMERICAN JOURNAL OF MATHEMATICS, 1956, 78 (02) :289-309
[9]  
Carbonaro A., 2013, PREPRINT
[10]   Conjugacy for Fourier-Bessel expansions [J].
Ciaurri, Oscar ;
Stempak, Krzysztof .
STUDIA MATHEMATICA, 2006, 176 (03) :215-247