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 12 p 23
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 Tntrntnetinn 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-stoppingerror 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 L12
7 Estimates for H1 x L L23
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, 1x 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
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