Differential and Integral Equations

Bounded holomorphic functional calculus for non-divergence form differential operators

Xuan Thinh Duong and Li Xin Yan

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Abstract

Let $L$ be a second-order elliptic partial differential operator of non-divergence form acting on ${\bf R^n}$ with bounded coefficients. We show that for each $1 < p_0 <2, L$ has a bounded $H_{\infty}$-functional calculus on $L^p({\bf R^n})$ for $p_0 <p <\infty$ if the $BMO$ norm of the coefficients is sufficiently small.

Article information

Source
Differential Integral Equations, Volume 15, Number 6 (2002), 709-730.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060813

Mathematical Reviews number (MathSciNet)
MR1893843

Zentralblatt MATH identifier
1020.47033

Subjects
Primary: 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)
Secondary: 35J15: Second-order elliptic equations 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 47A60: Functional calculus

Citation

Duong, Xuan Thinh; Yan, Li Xin. Bounded holomorphic functional calculus for non-divergence form differential operators. Differential Integral Equations 15 (2002), no. 6, 709--730. https://projecteuclid.org/euclid.die/1356060813


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