## Harmonic Analysis, Partial Differential Equations and Applications: In Honor of Richard L. WheedenSagun Chanillo, Bruno Franchi, Guozhen Lu, Carlos Perez, Eric T. Sawyer This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L. Wheeden made profound contributions. The papers deal with Weighted Norm inequalities for classical operators like Singular integrals, fractional integrals and maximal functions that arise in Harmonic Analysis. Other papers deal with applications of Harmonic Analysis to Degenerate Elliptic equations, variational problems, Several Complex variables, Potential theory, free boundaries and boundary behavior of functions. |

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### Contents

1 | |

The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity | 19 |

Weighted Inequalities of Poincaré Type on Chain Domains | 27 |

Homogenization and Applications to Mathematical Models in Medicine | 49 |

FormInvariance of Maxwell Equations in Integral Form | 69 |

ChernMoserWeyl Tensor and Embeddings into Hyperquadrics | 79 |

The Focusing EnergyCritical Wave Equation | 97 |

An Inverse Problem | 109 |

A Goodλ Lemma Two Weight T1 Theorems Without Weak Boundedness and a Two Weight Accretive Global Tb Theorem | 125 |

Intrinsic Difference Quotients | 165 |

Multilinear Weighted Norm Inequalities Under Integral Type Regularity Conditions | 193 |

Weighted Norm Inequalities of 1qType for Integral and Fractional Maximal Operators | 217 |

New Bellman Functions and Subordination by Orthogonal Martingales in Lp 1p2 | 239 |

Bounded Variation Convexity and AlmostOrthogonality | 275 |

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algebraic Anal apply assume balls Boman domains bounded Carnot groups Chanillo complementary subgroups condition convex Corollary cube Q defined Definition denote difference quotients dxdt dyadic elliptic embedding estimate Euclidean exists finite fractional integral Franchi graph grids Haar functions Harmonic Analysis Heisenberg groups Hence Hilbert transform Hölder's inequality holds holomorphic homogeneous hypersurfaces integral operator intrinsic Lipschitz kernel Lebesgue Lemma linear Lipschitz functions martingale Math Mathematics maximal function maximum principle measure metric Moreover Muckenhoupt multilinear nonnegative notation obtain orthogonal Poincaré inequalities pointwise Proof of Theorem Proposition prove quasicube Q quasimetric space R.L. Wheeden satisfies Sawyer singular integrals smooth ſº Sobolev Sobolev inequalities Sobolev space solutions subset Theorem 2.3 vector fields Volberg wave equation WBPT weighted norm inequalities