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Harmonic Analysis, Partial Differential Equations, Banach Spaces, and Operator Theory (Volume 2)

Part of the Association for Women in Mathematics Series Book Series (volume 5)

Editors: Pereyra, María Cristina; Marcantognini, Stefania; Stokolos, Alexander M.; Urbina, Wilfredo

DOI: 10.1007/978-3-319-51593-9

ISBN: 978-3-319-51591-5

Publisher: Springer International Publishing - Springer Journals

Jul 11, 2017

1 - 10 of 17 Chapters

LitStream

Remembering Corita…

Randall, Margaret

Pages: 3 –4

[Corita Sadosky—her mother’s name was Cora, so we called her Corita—was an Argentinean mathematician who belonged to her country’s “lost generation.” What that meant was that she came of age during the 1970s, dark years of dictatorship when 30,000 young people were murdered by neo-fascist forces...
LitStream

Remembering Cora

Hindman, Neil

Pages: 5 –7

[I spent almost three decades in an office adjacent to Cora’s office. We were in a building separate from the department office, where most of the Mathematics Department faculty had their offices. We were fortunate, since we had individual offices, while those in the other building had two or...
LitStream

The Two Weight Inequality for the Hilbert Transform: A Primer

Lacey, Michael T.

Pages: 11 –84

[Given a pair of weights w, σ, the two weight inequality for the Hilbert transform is of the form ∥H(σf)∥L2(w)≲∥f∥L2(σ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
LitStream

Singular Integrals, Rank One Perturbations and Clark Model in General Situation

Liaw, Constanze; Treil, Sergei

Pages: 85 –132

[We start with considering rank one self-adjoint perturbations Aα = A +α( ⋅ , φ)φ with cyclic vector φ∈ℌ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
LitStream

On Two Weight Estimates for Dyadic Operators

Beznosova, Oleksandra; Chung, Daewon; Moraes, Jean Carlo; Pereyra, María Cristina

Pages: 135 –169

[We provide a quantitative two weight estimate for the dyadic paraproduct πb under certain conditions on a pair of weights (u, v) and b in Carlu, v, a new class of functions that we show coincides with BMO when u = v ∈ A2d. We obtain quantitative two weight estimates for the dyadic square...
LitStream

Potential Operators with Mixed Homogeneity

Calderón, Calixto P.; Urbina, Wilfredo

Pages: 171 –181

[In 1966 Cora Sadosky introduced a number of results in a remarkable paper “A note on Parabolic Fractional and Singular Integrals”, see Sadosky (Studia Math 26:295–302, 1966), in particular, a quasi homogeneous version of Sobolev’s immersion theorem was discussed in the paper. Later, C. P....
LitStream

Elementary Proofs of One Weight Norm Inequalities for Fractional Integral Operators and Commutators

Cruz-Uribe, David

Pages: 183 –198

[We give new and elementary proofs of one weight norm inequalities for fractional integral operators and commutators. Our proofs are based on the machinery of dyadic grids and sparse operators used in the proof of the A2 conjecture.]
LitStream

Finding Cycles in Nonlinear Autonomous Discrete Dynamical Systems

Dmitrishin, Dmitriy; Khamitova, Anna; Stokolos, Alexander M.; Tohaneanu, Mihai

Pages: 199 –237

[The goal of this paper is to provide an exposition of recent results of the authors concerning cycle localization and stabilization in nonlinear dynamical systems. Both the general theory and numerical applications to well-known dynamical systems are presented. This paper is a continuation of...
LitStream

Smooth Analytic Functions and Model Subspaces

Dyakonov, Konstantin M.

Pages: 239 –266

[The main themes of this survey are as follows: (a) the canonical (Riesz–Nevanlinna) factorization in various classes of analytic functions on the disk that are smooth up to its boundary, and (b) model subspaces (i.e., invariant subspaces of the backward shift) in the Hardy spaces Hp and in BMOA....
LitStream

Rational Inner Functions on a Square-Matrix Polyball

Grinshpan, Anatolii; Kaliuzhnyi-Verbovetskyi, Dmitry S.; Vinnikov, Victor; Woerdeman, Hugo J.

Pages: 267 –277

[We establish the existence of a finite-dimensional unitary realization for every matrix-valued rational inner function from the Schur–Agler class on a unit square-matrix polyball. In the scalar-valued case, we characterize the denominators of these functions. We also show that a multiple of...

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