Bounded symbols and Reproducing Kernel Thesis for truncated Toeplitz operators

被引：61

作者：

Baranov, Anton ^{[2
]}

Chalendar, Isabelle ^{[1
]}

Fricain, Emmanuel ^{[1
]}

Mashreghi, Javad ^{[3
]}

Timotin, Dan ^{[4
]}

机构：

[1] Univ Lyon 1, INSA Lyon, Ecole Cent Lyon, Inst Camille Jordan,CNRS,UMR5208, F-69622 Villeurbanne, France

[2] St Petersburg State Univ, Dept Math & Mech, St Petersburg 198504, Russia

[3] Univ Laval, Dept Math & Stat, Quebec City, PQ G1K 7P4, Canada

[4] Romanian Acad, Inst Math, Bucharest 014700, Romania

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 259卷 / 10期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Toeplitz operators; Reproducing Kernel Thesis; Model spaces; CLASS HANKEL-OPERATORS; CARLESON EMBEDDINGS; MEAN-OSCILLATION; RADIAL LIMITS;

D O I：

10.1016/j.jfa.2010.05.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Compressions of Toeplitz operators to coinvariant subspaces of H-2 are called truncated Toeplitz operators. We study two questions related to these operators. The first, raised by Sarason, is whether boundedness of the operator implies the existence of a bounded symbol; the second is the Reproducing Kernel Thesis. We show that in general the answer to the first question is negative, and we exhibit some classes of spaces for which the answers to both questions are positive. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：2673 / 2701

页数：29

共 33 条

[1] RADIAL LIMITS AND INVARIANT SUBSPACES [J].

AHERN, PR ;

CLARK, DN .

AMERICAN JOURNAL OF MATHEMATICS, 1970, 92 (02) :332-&

[2] On embedding theorems for coinvariant subspaces of the shift operator. II [J].

Aleksandrov A.B. .

Journal of Mathematical Sciences, 2002, 110 (5) :2907-2929

[3]

[Anonymous], 1981, BOUNDED ANAL FUNCTIO

[4]

[Anonymous], 1986, GRUNDLEHREN MATH WIS

[5] THE BERGMAN SPACE, THE BLOCH SPACE, AND COMMUTATORS OF MULTIPLICATION OPERATORS [J].

AXLER, S .

DUKE MATHEMATICAL JOURNAL, 1986, 53 (02) :315-332

[6]

Axler S., 1978, INTEREQU OPER TH, V1, P285, DOI [10.1007/BF01682841, DOI 10.1007/BF01682841]

[7] On an extension problem for polynomials [J].

Bakonyi, M ;

Timotin, D .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2001, 33 :599-605

[8] BOUNDEDNESS OF HANKEL-MATRICES [J].

BONSALL, FF .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1984, 29 (APR) :289-300

[9]

Brown A., 1964, J. Reine. Angew. Math, V213, P89

[10]

CIMA J, INDIANA U M IN PRESS

← 1 2 3 4 →