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 K?oz?o 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
