Hiroshima Mathematical Journal

Compact Toeplitz operators on parabolic Bergman spaces

Masaharu Nishio, Noriaki Suzuki, and Masahiro Yamada

Full-text: Open access

Abstract

Parabolic Bergman space $\berg[p]$ is a Banach space of all $p$-th integrable solutions of a parabolic equation $(\partial/\partial t + (-\Delta)^{\alpha})u = 0$ on the upper half space, where $0<\alpha\leq1$ and $1\leq p<\infty$. In this note, we consider the Toeplitz operator from $\berg[p]$ to $\berg[q]$ where $p\leq q$, and discuss the condition that it be compact.

Article information

Source
Hiroshima Math. J., Volume 38, Number 2 (2008), 177-192.

Dates
First available in Project Euclid: 5 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1220619455

Digital Object Identifier
doi:10.32917/hmj/1220619455

Mathematical Reviews number (MathSciNet)
MR2437569

Zentralblatt MATH identifier
1172.35338

Subjects
Primary: 35K05: Heat equation
Secondary: 31B10: Integral representations, integral operators, integral equations methods 26D10: Inequalities involving derivatives and differential and integral operators

Keywords
Carleson measure Toeplitz operator heat equation parabolic operator of fractional order Bergman space compact operator

Citation

Nishio, Masaharu; Suzuki, Noriaki; Yamada, Masahiro. Compact Toeplitz operators on parabolic Bergman spaces. Hiroshima Math. J. 38 (2008), no. 2, 177--192. doi:10.32917/hmj/1220619455. https://projecteuclid.org/euclid.hmj/1220619455


Export citation