## Advances in Analysis: The Legacy of Elias M. SteinPrinceton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. His fundamental contributions include the Kunze-Stein phenomenon, the construction of new representations, the Stein interpolation theorem, the idea of a restriction theorem for the Fourier transform, and the theory of Hp Spaces in several variables. Through his great discoveries, through books that have set the highest standard for mathematical exposition, and through his influence on his many collaborators and students, Stein has changed mathematics. Drawing inspiration from Stein’s contributions to harmonic analysis and related topics, this volume gathers papers from internationally renowned mathematicians, many of whom have been Stein’s students. The book also includes expository papers on Stein’s work and its influence. The contributors are Jean Bourgain, Luis Caffarelli, Michael Christ, Guy David, Charles Fefferman, Alexandru D. Ionescu, David Jerison, Carlos Kenig, Sergiu Klainerman, Loredana Lanzani, Sanghyuk Lee, Lionel Levine, Akos Magyar, Detlef Müller, Camil Muscalu, Alexander Nagel, D. H. Phong, Malabika Pramanik, Andrew S. Raich, Fulvio Ricci, Keith M. Rogers, Andreas Seeger, Scott Sheffield, Luis Silvestre, Christopher D. Sogge, Jacob Sturm, Terence Tao, Christoph Thiele, Stephen Wainger, and Steven Zelditch. |

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### Contents

A Case Study | 35 |

Hölder Regularity for Generalized Master Equations with | 63 |

Extremizers of a Radon Transform Inequality | 84 |

Should We Solve Plateaus Problem Again? | 108 |

Averages along Polynomial Sequences in Discrete Nilpotent | 146 |

Internal DLA for Cylinders | 189 |

The Energy Critical Wave Equation in 3D | 215 |

On DivCurl for Higher Order | 245 |

CONTENTS | 273 |

Problems of Harmonic Analysis Related to FiniteType | 303 |

MultiLinear Multipliers Associated to Simplexes of Arbitrary | 346 |

Diagonal Estimates for Bergman Kernels in MonomialType | 402 |

On the Singularities of the Pluricomplex Greens Function | 419 |

Smoothness of Spectral Multipliers and Convolution Kernels | 436 |

List of Contributors | 463 |