STRICHARTZ AND SMOOTHING ESTIMATES FOR DISPERSIVE SEMI-GROUP ${\rm e}^{-{\rm i} t P(D)}$ IN WEIGHTED ${ L}^{2}$ SPACES AND THEIR APPLICATIONS

doi:10.1007/s10473-025-0208-5

Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (2): 401-415.doi: 10.1007/s10473-025-0208-5

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STRICHARTZ AND SMOOTHING ESTIMATES FOR DISPERSIVE SEMI-GROUP ${\rm e}^{-{\rm i} t P(D)}$ IN WEIGHTED ${ L}^{2}$ SPACES AND THEIR APPLICATIONS

Jiecheng Chen, Shaolei Ru, Chenjing Wu^*

Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Received:2023-03-02 Revised:2024-03-18 Online:2025-03-25 Published:2025-05-08
Contact: *Chenjing wu, E-mail: CJWu.jx@zjnu.edu.cn
About author:Jiecheng Chen, E-mail: jcchen@zjnu.edu.cn; Jiecheng Chen, E-mail: rushaolei@zjnu.edu.cn
Supported by:
Fun:The research was supported by the NSFC (12071437) and the National Key R& D Program of China (2022YFA1005700).

Abstract

Abstract: Combining $TT^{\ast}$ argument and bilinear interpolation, this paper obtains the Strichartz and smoothing estimates of dispersive semi-group ${\rm e}^{-{\rm i} t P(D)}$ in weighted $L^{2}$ spaces. Among other things, we recover the results in [1]. Moreover, the application of these results to the well-posedness of some equations are shown in the last section.

Key words: Strichartz estimates, smoothing estimates, Morrey-Campanato class, weighted $L^{2}$ spaces, well-posedness

CLC Number:

35B45

Jiecheng Chen, Shaolei Ru, Chenjing Wu. STRICHARTZ AND SMOOTHING ESTIMATES FOR DISPERSIVE SEMI-GROUP ${\rm e}^{-{\rm i} t P(D)}$ IN WEIGHTED ${ L}^{2}$ SPACES AND THEIR APPLICATIONS[J].Acta mathematica scientia,Series B, 2025, 45(2): 401-415.

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STRICHARTZ AND SMOOTHING ESTIMATES FOR DISPERSIVE SEMI-GROUP ${\rm e}^{-{\rm i} t P(D)}$ IN WEIGHTED ${ L}^{2}$ SPACES AND THEIR APPLICATIONS

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