Characterization of UMD Banach Spaces by Imaginary Powers of Hermite and Laguerre Operators

被引：5

作者：

Betancor, Jorge J. ^{[1
]}

Castro, Alejandro J. ^{[1
]}

Curbelo, Jezabel ^{[2
]}

Rodriguez-Mesa, Lourdes ^{[1
]}

机构：

[1] Univ La Laguna, Dept Anal Matemat, San Cristobal la Laguna 38271, Sta Cruz De Ten, Spain

[2] CSIC, Inst Ciencias Matemat CSIC UAM UCM UC3M, E-28049 Madrid, Spain

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2013年 / 7卷 / 04期

关键词：

Laguerre operator; Laplace transform type multipliers; UMD spaces; Imaginary powers; LAPLACE TRANSFORM TYPE; FUNCTION EXPANSIONS; RIESZ TRANSFORMS; SPECTRAL MULTIPLIERS; POISSON INTEGRALS;

D O I：

10.1007/s11785-011-0203-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we characterize the Banach spaces with the UMD property by means of L (p) -boundedness properties for the imaginary powers of the Hermite and Laguerre operators. In order to do this we need to obtain pointwise representations for the Laplace transform type multipliers associated with Hermite and Laguerre operators.

引用

页码：1019 / 1048

页数：30

共 50 条

[41] A MULTIPLIER CHARACTERIZATION OF ANALYTIC UMD SPACES
BLOWER, G
STUDIA MATHEMATICA, 1990, 96 (02) : 117 - 124
[42] Examples of pseudo-differential operators in L(p) spaces with unbounded imaginary powers
Hieber, M
ARCHIV DER MATHEMATIK, 1996, 66 (02) : 126 - 131
[43] Martingale decompositions and weak differential subordination in UMD Banach spaces
Yaroslavtsev, Ivan S.
BERNOULLI, 2019, 25 (03) : 1659 - 1689
[44] γ-Radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces
Betancor, J. J.
Castro, A. J.
Curbelo, J.
Farina, J. C.
Rodriguez-Mesa, L.
JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (12) : 3804 - 3856
[45] Infinitely delayed stochastic evolution equations on UMD Banach spaces
Crewe, Paul
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 415 (01) : 325 - 345
[46] Randomized UMD Banach spaces and decoupling inequalities for stochastic integrals
Veraar, Mark C.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (05) : 1477 - 1486
[47] On Banach spaces with small spaces of operators
Zsák, A
TRENDS IN BANACH SPACES & OPERATOR THEORY, 2003, 321 : 347 - 369
[48] Banach spaces with small spaces of operators
Gowers, WT
Maurey, B
MATHEMATISCHE ANNALEN, 1997, 307 (04) : 543 - 568
[49] Banach spaces with small spaces of operators
W. T. Gowers
B. Maurey
Mathematische Annalen, 1997, 307 : 543 - 568
[50] On Schrodinger Groups of Fractional Powers of Hermite Operators
Bui, The Anh
Duong, Xuan Thinh
Hong, Qing
Hu, Guorong
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (07) : 6164 - 6185

← 1 2 3 4 5 →