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February 2010 A conjugate system and tangential derivative norms on parabolic Bergman spaces
Yosuke HISHIKAWA, Masaharu NISHIO, Masahiro YAMADA
Hokkaido Math. J. 39(1): 85-114 (February 2010). DOI: 10.14492/hokmj/1274275021

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 ${\boldsymbol b}_{\alpha}^{p}(\lambda)$.

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Yosuke HISHIKAWA. Masaharu NISHIO. Masahiro YAMADA. "A conjugate system and tangential derivative norms on parabolic Bergman spaces." Hokkaido Math. J. 39 (1) 85 - 114, February 2010. https://doi.org/10.14492/hokmj/1274275021

Information

Published: February 2010
First available in Project Euclid: 19 May 2010

zbMATH: 1218.35115
MathSciNet: MR2649328
Digital Object Identifier: 10.14492/hokmj/1274275021

Subjects:
Primary: 35K05
Secondary: 26D10, 42A50

Rights: Copyright © 2010 Hokkaido University, Department of Mathematics

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Vol.39 • No. 1 • February 2010
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