Tokyo Journal of Mathematics

Generalized Besov Spaces and Their Applications

Takeshi KAWAZOE and Hatem MEJJAOLI

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Abstract

We define and study the Bessel potential and inhomogeneous Besov spaces associated with the Dunkl operators on $\mathbf{R}^d$. As applications on these spaces we construct the Sobolev type embedding theorem and the paraproduct operators associated with the Dunkl operators, as similar to those defined by Bony. We also establish Strichartz type estimates for the Dunkl-Schrödinger equation and finally we study the problem of well posedness of the generalized heat equation.

Article information

Source
Tokyo J. Math., Volume 35, Number 2 (2012), 297-320.

Dates
First available in Project Euclid: 23 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1358951320

Digital Object Identifier
doi:10.3836/tjm/1358951320

Mathematical Reviews number (MathSciNet)
MR3058708

Zentralblatt MATH identifier
1331.35296

Subjects
Primary: 35L05: Wave equation
Secondary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 35J25: Boundary value problems for second-order elliptic equations 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]

Citation

KAWAZOE, Takeshi; MEJJAOLI, Hatem. Generalized Besov Spaces and Their Applications. Tokyo J. Math. 35 (2012), no. 2, 297--320. doi:10.3836/tjm/1358951320. https://projecteuclid.org/euclid.tjm/1358951320


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References

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