Generalized besov spaces and their applications

Takeshi Kawazoe; Hatem Mejjaoli

doi:10.3836/tjm/1358951320

Generalized besov spaces and their applications

Takeshi Kawazoe, Hatem Mejjaoli

Faculty of Policy Management

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We define and study the Bessel potential and inhomogeneous Besov spaces associated with the Dunkl operators on 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.

Original language	English
Pages (from-to)	297-320
Number of pages	24
Journal	Tokyo Journal of Mathematics
Volume	35
Issue number	2
DOIs	https://doi.org/10.3836/tjm/1358951320
Publication status	Published - 2012 Dec

Keywords

Differential-difference equations
Dunkl operators
Inhomogeneous dunkl-besov space
Inhomogeneous dunkl-triebel-lizorkin space
Littlewood-Paley decomposition
Paraproduct operator

ASJC Scopus subject areas

Mathematics(all)

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10.3836/tjm/1358951320

Cite this

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title = "Generalized besov spaces and their applications",

abstract = "We define and study the Bessel potential and inhomogeneous Besov spaces associated with the Dunkl operators on Rd. 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-Schr{\"o}dinger equation and finally we study the problem of well posedness of the generalized heat equation.",

keywords = "Differential-difference equations, Dunkl operators, Inhomogeneous dunkl-besov space, Inhomogeneous dunkl-triebel-lizorkin space, Littlewood-Paley decomposition, Paraproduct operator",

author = "Takeshi Kawazoe and Hatem Mejjaoli",

year = "2012",

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doi = "10.3836/tjm/1358951320",

language = "English",

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AU - Kawazoe, Takeshi

AU - Mejjaoli, Hatem

PY - 2012/12

Y1 - 2012/12

N2 - We define and study the Bessel potential and inhomogeneous Besov spaces associated with the Dunkl operators on Rd. 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.

AB - We define and study the Bessel potential and inhomogeneous Besov spaces associated with the Dunkl operators on Rd. 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.

KW - Differential-difference equations

KW - Dunkl operators

KW - Inhomogeneous dunkl-besov space

KW - Inhomogeneous dunkl-triebel-lizorkin space

KW - Littlewood-Paley decomposition

KW - Paraproduct operator

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SP - 297

EP - 320

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

IS - 2

ER -

Generalized besov spaces and their applications

Abstract

Keywords

ASJC Scopus subject areas

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