Some Topics in Harmonic Analysis and Applications(調(diào)和分析與應(yīng)用中的一些問題)
定 價(jià):98 元
- 作者:李俊峰 等主編
- 出版時(shí)間:2015/8/1
- ISBN:9787040430189
- 出 版 社:高等教育出版社
- 中圖法分類:O241.86
- 頁碼:422
- 紙張:膠版紙
- 版次:1
- 開本:16開
陸善鎮(zhèn)教授專攻調(diào)和分析及其應(yīng)用,特別是在Bochner-Riesz平均、奇異積分和振蕩積分算子有界性以及函數(shù)空間理論方面做出了重要的貢獻(xiàn)。他培養(yǎng)了一大批優(yōu)秀的中青年數(shù)學(xué)工作者并成為中國調(diào)和分析及其應(yīng)用領(lǐng)域的中堅(jiān)力量。陸先生曾擔(dān)任北京師范大學(xué)校長,現(xiàn)擔(dān)任溫州-肯恩大學(xué)校長。李俊峰、李曉春、陸國震編寫的《調(diào)和分析及其應(yīng)用中的一些問題(英文版)(精)》內(nèi)容定位于陸善鎮(zhèn)教授做出重要成就及感興趣的領(lǐng)域,匯集了多位國際著名數(shù)學(xué)家以及陸先生的朋友和學(xué)生撰寫的學(xué)術(shù)論文,包括了Calderón-Zygmund奇異積分算子理論以及局部Tb定理、多線性奇異積分算子和Fourier乘子理論、多線性嵌入定理、流形上特征函數(shù)的模估計(jì)、帶權(quán)不等式、非線性Schrodinger方程、函數(shù)空間理論等方面的一些問題的最新進(jìn)展。本書將有益于調(diào)和分析及其相關(guān)領(lǐng)域的研究者以及碩士生、博士生。
Multilinear Embedding and Hardy's Inequality
William Beckner
1 Multilinear convolution inequalities
2 Diagonal trace restriction for Hardy's inequality
3 Diagonal trace restriction for a multilinear fractional integral
4 Multilinear integrals and rearrangement
Acknowledgements
References
Real-variable Theory of Orlicz-type Function Spaces Associated
with Operators -- A Survey
Der-Chen Chang, Dachun Yang and Sibei Yang
1 Introduction
2 Orlicz type spaces associated with operators satisfying Poisson
estimates
3 Musielak-Orlicz type spaces associated with nonnegative self-adjoint
operators satisfying Davies-Gaffney estimates
4 Musielak-Orlicz type spaces associated with operators satisfying
bounded Ha-functional calculus
Acknowledgements
References
Boundedness of Rough Strongly Singular Integral Operators
Jiecheng Chen, Dashan Fan and Meng Wang
1 Lp --+ Lq boundedness on rough operators
2 The phase function is not radial
3 The kernel satisfies a Lipschitz condition
4 The kernel is Ca
References
On the Dimension Dependence of Some Weighted Inequalities
Alberto Criado and Fernando Soria
1 Introduction
2 The maximal operator over radial functions
3 Proofs of the main results
4 Kakeya maximal operator
Acknowledgements
References
Lp Estimates for Multi-parameter and Multilinear Fourier
Multipliers and Pseudo-differential Operators
Wei Dai, Guozhen Lu and Lu Zhang
1 Introduction
2 Lp estimates for multi-parameter and multi-linear paraproducts,
multipliers and pseudo-differential operators
3 Lp estimates for bilinear and multi-parameter Hilbert transforms . .
4 Lp estimates for bilinear operators given by non-smooth symbols with
one-dimensional singularity set in the range 1/2 < p < 2/3
Acknowledgements
References
Existence and Uniqueness Theory for the Fractional SchrSdinger
Equation on the Torus
Seckin Demirbas, M. Burak Erdoan and Nikolaos Tzirakis
1 Introduction
2 Notation and preliminaries
3 Strichartz estimates
4 Local well-posedness via the X8,b method
5 A smoothing estimate
6 Global well-posedness via high-low frequency decomposition
References
Compactness of Maximal Commutators of Bilinear
Calder6n-Zygmund Singular Integral Operators
Yong Ding, Ting Mei and Qingying Xue
1 Tntrn(tnetinn nH rn r,It
2 The proof of Theorem 1.1
3 The proof of Theorem 1.2
References
Weak Hardy Spaces
Loukas Grafakos and Danqing He
1 Introduction
2 Relevant background
3 The proof of Theorem 1
4 Properties of Hp'
5 Square function characterization of Hp'
References
A Local Tb Theorem with Vector-valued Testing Functions...
Ana Grau de la Herren and Steve Hofmann
1 Introduction, history, preliminaries
2 A local Tb theorem with vector-valued testing functions
3 Application of Theorem 2.13 to the theory of layer potentials .
4 Appendix: a generalized Christ-Journ@ T1 Theorem for square
functions
References
Non-homogeneous Local T1 Theorem" Dual Exponents
Michael T. Lacey and Antti V. Vdhdkangas
1 Introduction
2 Preliminaries
3 Perturbations and a basic decomposition
4 A stopping tree construction
5 The inside-paraproduct term
6 The inside-stopping/error term
7 The separated term
8 Preparations for the nearby term
9 The nearby-non-boundary term
10 The nearby-boundary term
References
The Dynamics of the NLS with the Combined Terms in Five and
Higher Dimensions
Changxing Miao, Guixiang Xu and Lifeng Zhao
1 Introduction
2 Preliminaries
3 Variational characterization
4 Part I: blow up for K:- .
5 Profile decomposition
6 Part II: GWP and scattering for ]C+
Acknowledgements
References
Sharp Estimates for Bilinear Fourier Multiplier Operators
Akihiko Miyachi and Naohito Tomita
1 Introduction
2 Product type Sobolev scale
3 Estimates for L2 x L --, L2
4 Estimates for H1 x L -- L1
5 Estimates for L x L --, BMO
6 Estimates for H1 x H1 L1/2
7 Estimates for H1 x L L2/3
8 Proof of the only if part
9 Isotropic Besov scale
References
Weighted Estimates for Fractional Type Marcinkiewicz Integral
Operators Associated to Surfaces
Yoshihiro Sawano and KSz6 Yabuta
1 Introduction
2 Preparation for the proof of Theorem 3
3 Proof of Theorem 3
4 Proof of Proposition 1
5 Appendix: complex interpolation of homogeneous weighted
Triebel-Lizorkin spaces
References
Commutator Estimates for the Dirichlet-to-Neumann Map in
Lipschitz Domains
Zhongwei Shen
1 Introduction
2 Dahlberg's bilinear estimate, Part I
3 Dahlberg's bilinear estimate, Part II
4 Trilinear estimates and proof of Theorem 1.1
5 Proof of Theorem 1.2
References
A Note on LP-norms of Quasi-modes
Christopher D. Sogge and Steve Zelditch
1 Introduction and main results
2 Proof that Proposition 1.3 implies Theorems 1.1 and 1.2
3 Proof of Proposition 1.3
4 Applications to breaking convexity bounds
References
Astalas Conjecture from the Point of View of Singular Integrals
on Metric Spaces
Alexander Volberg
1 Introduction
2 A simple proof of Theorem 1. The weighted estimate of
Ahlfors-Beurling transform = unweighted estimate of a certain
non-symmetric Calder6n-Zygmund operator on a metric space . . .
3 T1 theorem for non-homogeneous metric measure spaces
Acknowledgements
References
C.S.I. for Besov Spaces P'q(]) with (a, (p,q)) e (0, 1)x ((0, 1]x
(0,1] \ {(1,1)})
Jie Xiao and Zhiehun Zhai
1 Introduction
2 C.S.I
3 Applications
Acknowledgements
References
A List of Ph.D. Students Post-doctors and Visiting Scholars
Supervised by Professor Shanzhen Lu and Foreign Collaborators
Who Worked with Professor Shanzhen Lu