Sobolev spaces associated to the harmonic oscillator

被引：77

作者：

Bongioanni, B. ^{[1
]}

Torrea, J. L.

机构：

[1] Univ Nacl Litoral, Fac Ingn Qim, Dept Matemat, RA-3000 Santa Fe, Argentina

[2] Inst Matemat Aplicada Litoral, RA-3000 Santa Fe, Argentina

[3] Univ Autonoma Madrid, Fac Ciencias, Dept Matemat, E-28049 Madrid, Spain

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2006年 / 116卷 / 03期

关键词：

Hermite operator; potential spaces; Riesz transforms;

D O I：

10.1007/BF02829750

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator H = -Delta + \x\(2). Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrodinger equation are also considered.

引用

页码：337 / 360

页数：24

共 14 条

[1]

Carleson L., 1980, Euclidean harmonic analysis, V779, P5, DOI DOI 10.1007/BFB0087666

[2]

COWLING MG, 1983, LECT NOTES MATH, V992, P83

[3]

Dahlberg C. E., 1982, Harmonic analysis, V908, P205, DOI DOI 10.1007/BFB0093289

[4]

Folland G.B., 1984, REAL ANAL MODERN TEC

[5] Lp-dimension free boundedness for Riesz transforms associated to Hermite functions [J].

Harboure, E ;

de Rosa, L ;

Segovia, C ;

Torrea, JL .

MATHEMATISCHE ANNALEN, 2004, 328 (04) :653-682

[6] Schrodinger equation and the oscillatory semigroup for the Hermite operator [J].

Nandakumaran, AK ;

Ratnakumar, PK .

JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 224 (02) :371-385

[7]

RADHA R, 2004, J ANAL, V12, P183

[8]

Stein E M., 1993, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals

[9]

Stein E. M., 1970, SINGULAR INTEGRALS D

[10] Poisson integrals and Riesz transforms for Hermite function expansions with weights [J].

Stempak, K ;

Torrea, JL .

JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 202 (02) :443-472

← 1 2 →