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 sca