## Hokkaido Mathematical Journal

### A conjugate system and tangential derivative norms on parabolic Bergman spaces

#### Abstract

The $\alpha$-parabolic Bergman space ${\boldsymbol b}_{\alpha}^{p}(\lambda)$ is the Banach space of solutions of the parabolic equation $L^{(\alpha)} = \partial/\partial t+(-\Delta_{x})^{\alpha}$ on the upper half space $H$ which have finite $L^{p}(H,t^{\lambda}dV)$ norms, where $t^{\lambda}dV$ is the weighted Lebesgue volume measure on $H$. It is known that ${\boldsymbol b}^{p}_{1/2}(\lambda)$ coincide with the harmonic Bergman spaces. In this paper, we introduce the extension of notion of conjugate functions of ${\boldsymbol b}_{\alpha}^{p}(\lambda)$-functions and study their properties. As an application, we give estimates of tangential derivative norms on ${\boldsymbol b}_{\alpha}^{p}(\lambda)$.

#### Article information

Source
Hokkaido Math. J., Volume 39, Number 1 (2010), 85-114.

Dates
First available in Project Euclid: 19 May 2010

https://projecteuclid.org/euclid.hokmj/1274275021

Digital Object Identifier
doi:10.14492/hokmj/1274275021

Mathematical Reviews number (MathSciNet)
MR2649328

Zentralblatt MATH identifier
1218.35115

#### Citation

HISHIKAWA, Yosuke; NISHIO, Masaharu; YAMADA, Masahiro. A conjugate system and tangential derivative norms on parabolic Bergman spaces. Hokkaido Math. J. 39 (2010), no. 1, 85--114. doi:10.14492/hokmj/1274275021. https://projecteuclid.org/euclid.hokmj/1274275021