## Nagoya Mathematical Journal

### Notes on boundedness of spectral multipliers on Hardy spaces associated to operators

Bui The Anh

#### Abstract

Let $L$ be a nonnegative self-adjoint operator on $L^{2}(X)$, where $X$ is a space of homogeneous type. Assume that $L$ generates an analytic semigroup $e^{-tL}$ whose kernel satisfies the standard Gaussian upper bounds. We prove that the spectral multiplier $F(L)$ is bounded on $H^{p}_{L}(X)$ for $0\textless p\leq1$, the Hardy space associated to operator $L$, when $F$ is a suitable function.

#### Article information

Source
Nagoya Math. J., Volume 203 (2011), 109-122.

Dates
First available in Project Euclid: 18 August 2011

https://projecteuclid.org/euclid.nmj/1313682314

Digital Object Identifier
doi:10.1215/00277630-1331881

Mathematical Reviews number (MathSciNet)
MR2834251

Zentralblatt MATH identifier
1228.42014

Subjects
Primary: 34L05: General spectral theory 30H10: Hardy spaces

#### Citation

Anh, Bui The. Notes on boundedness of spectral multipliers on Hardy spaces associated to operators. Nagoya Math. J. 203 (2011), 109--122. doi:10.1215/00277630-1331881. https://projecteuclid.org/euclid.nmj/1313682314

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