Hokkaido Mathematical Journal

NISHIO Masaharu, SUZUKI Noriaki, YAMADA Masahiro,

Toeplitz operators and Carleson measures on parabolic Bergman spaces.

Hokkaido Mathematical Journal, 36 (2007) pp.563-583

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Abstract

Let $\boldsymbol b^p_\alpha$ be the parabolic Bergman space, which is the Banach space of all $L^p$-solutions of the parabolic equation $(\partial/\partial t + (-\Delta)^{\alpha})u = 0$ on the upper half space $\boldsymbol R^{n+1}_+$ with $0 < \alpha \leq 1$. We discuss the relation of Toeplitz operators to Carleson measures.

MSC(Primary)35K05
MSC(Secondary)31B10, 26D10
Uncontrolled KeywordsCarleson measure, Toeplitz operator, heat equation, parabolic operator of fractional order, Bergman space