Some Topics in Harmonic Analysis and Applications

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