Extended Cesaro operators between different Hardy spaces

被引：55

作者：

Avetisyan, Karen ^{[2
]}

Stevic, Stevo ^{[1
]}

机构：

[1] Serbian Acad Sci, Math Inst, Belgrade 11000, Serbia

[2] Yerevan State Univ, Fac Phys, Yerevan 375025, Armenia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 207卷 / 02期

关键词：

Extended Cesaro operators; Unit ball; Hardy space; Bloch space; Boundedness; Compactness; RIEMANN-STIELTJES OPERATORS; INTEGRAL-TYPE OPERATORS; MIXED-NORM SPACES; BLOCH-TYPE SPACES; UNIT BALL; H-INFINITY; COMPACTNESS; BOUNDEDNESS; PRODUCTS;

D O I：

10.1016/j.amc.2008.10.055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Hp denote the Hardy space of holomorphic functions on the unit ball B. This note gives some sufficient and necessary conditions for the boundedness and compactness of the following extended Cesaro operators T(g)f(z) = integral(1)(0) f(tz)Rg(tz)dt/t and L(g)f(z) = integral(1)(0) Rf(tz)g(tz)dt/t, where z is an element of B and g is a fixed holomorphic map on B, acting from the space H-p into the space H-q, for the case p < q. Our results extend and simplify some one-dimensional results. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：346 / 350

页数：5

共 34 条

[1] An integral operator on Hp and Hardy's inequality [J].

Aleman, A ;

Cima, JA .

JOURNAL D ANALYSE MATHEMATIQUE, 2001, 85 (1) :157-176

[2]

Beatrous F., 1989, DISSERTATIONES MATH

[3] A note on weighted Bergman spaces and the Cesaro operator (vol 159, pg 25, 2000) [J].

Chang, DC ;

Stevic, S .

NAGOYA MATHEMATICAL JOURNAL, 2005, 180 :77-90

[4]

Chang DC, 2003, TAIWAN J MATH, V7, P423

[5]

Chang DC, 2003, TAIWAN J MATH, V7, P293

[6] On some integral operators on the unit polydisk and the unit ball [J].

Chang, Der-Chen ;

Li, Songxiao ;

Stevic, Stevo .

TAIWANESE JOURNAL OF MATHEMATICS, 2007, 11 (05) :1251-1285

[7] Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball [J].

Clahane, Dana D. ;

Stevic, Stevo .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2006, 2006 (1)

[8] Extended Cesaro operators on Bergman spaces [J].

Hu, ZJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 296 (02) :435-454

[9] Extended Cesaro operators on mixed norm spaces [J].

Hu, ZJ .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (07) :2171-2179

[10] Extended Cesaro operators on the Bloch space in the unit ball of Cn [J].

Hu, ZJ .

ACTA MATHEMATICA SCIENTIA, 2003, 23 (04) :561-566

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