陆善镇教授专攻调和分析及其应用，特别是在Bochner-Riesz平均、奇异积分和振荡积分算子有界性以及函数空间理论方面做出了重要的贡献。他培养了一大批优秀的中青年数学工作者并成为中国调和分析及其应用领域的中坚力量。陆先生曾担任北京师范大学校长，现担任温州-肯恩大学校长。本书内容定位于陆善镇教授做出重要成就及感兴趣的领域，汇集了多位国际著名数学家以及陆先生的朋友和学生撰写的学术论文，包括了Calderón-Zygmund奇异积分算子理论以及局部Tb定理、多线性奇异积分算子和Fourier乘子理论、多线性嵌入定理、流形上特征函数的模估计、带权不等式、非线性Schrödinger方程、函数空间理论等方面的一些问题的最新进展。本书将有益于调和分析及其相关领域的研究者以及硕士生、博士生。
- 前辅文
- 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 H∞-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 ThekernelisC∞
- 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 Schr¨odinger Equation on the Torus
- Seckin Demirbas, MBurak Erdo˘gan and Nikolaos Tzirakis
- 1 Introduction
- 2 Notation and preliminaries
- 3 Strichartz estimates
- 4 Local well-posedness via the Xs,b method
- 5 A smoothing estimate
- 6 Global well-posedness via high-low frequency decomposition
- References
- Compactness of Maximal Commutators of Bilinear Calder′on-Zygmund Singular Integral Operators
- Yong Ding, Ting Mei and Qingying Xue
- 1 Introduction and main results
- 2 The proof of Theorem1.1
- 3 The proof of Theorem1.2
- References
- Weak Hardy Spaces
- Loukas Grafakos and Danqing He
- 1 Introduction
- 2 Relevant background
- 3 The proof of Theorem1
- 4 Properties of Hp,∞
- 5 Square function characterization of Hp,∞
- References
- A Local Tb Theorem with Vector-valued Testing Functions
- Ana Grau de la Herr´an and Steve Hofmann
- 1 Introduction, history, preliminaries
- 2 Alocal 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´e T 1 Theorem for square
- functions
- References
- Non-homogeneous Local T 1 Theorem: Dual Exponents
- Michael TLacey and Antti VV¨ah¨akangas
- 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 K+
- Acknowledgements
- References
- Sharp Estimates for Bilinear Fourier Multiplier Operators
- Akihiko Miyachi and Naohito Tomita
- 1 Introduction
- 2 Product type Sobolev scale
- 3 EstimatesforL2 × L∞ → L2
- 4 EstimatesforH1 × L∞ → L1
- 5 EstimatesforL∞ × L∞ → BMO
- 6 EstimatesforH1 × H1 → L1/2
- 7 EstimatesforH1 × L2 → 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 Kˆozˆo Yabuta
- 1 Introduction
- 2 Preparation for the proof of Theorem3
- 3 Proof of Theorem3
- 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 Theorem1.2
- References
- A Note on Lp-norms of Quasi-modes
- Christopher DSogge 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
- Astala’s Conjecture from the Point of View of Singular Integrals on Metric Spaces
- Alexander Volberg
- 1 Introduction
- 2 A simple proof of Theorem 1The weighted estimate of Ahlfors-Beurling transform = unweighted estimate of a certain non-symmetric Calder´on-Zygmund operator on a metric space
- 3 T 1 theorem for non-homogeneous metric measure spaces
- Acknowledgements
- References
- C.S.Ifor Besov Spaces ˙Λp,qα (Rn) with _α, (p, q)_ ∈ (0, 1) × _(0, 1]×(0, 1] \ {(1, 1)}_
- Jie Xiao and Zhichun Zhai
- 1 Introduction
- 2 C.S.I
- 3 Applications
- Acknowledgements
- References
- A List of Ph.DStudents, Post-doctors and Visiting Scholars Supervised by Professor Shanzhen Lu and Foreign Collaborators Who Worked with Professor Shanzhen Lu
