Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform
نویسنده
چکیده
This paper is devoted to the proof of two related results. The first one asserts that if μ is a Radon measure in R satisfying lim sup r→0 μ(B(x, r)) r > 0 and ∫ 1
منابع مشابه
Lecture notes on rectifiable sets, densities, and tangent measures
Contents Chapter 1. Introduction 5 Chapter 2. Notation and preliminaries 9 1. General notation and measures 9 2. Weak * convergence of measures 10 3. Covering theorems and differentiation of measures 13 4. Hausdorff measures 13 5. Lipschitz functions 15 6. The Stone–Weierstrass Theorem 16 Chapter 3. Marstrand's Theorem and tangent measures 17 1.
متن کاملOn the Cauchy Problem for Hartree Equation in the Wiener Algebra
We consider the mass-subcritical Hartree equation with a homogeneous kernel, in the space of square integrable functions whose Fourier transform is integrable. We prove a global well-posedness result in this space. On the other hand, we show that the Cauchy problem is not even locally wellposed if we simply work in the space of functions whose Fourier transform is integrable. Similar results ar...
متن کامل2 Generalized Cauchy - Stieltjes Transforms and Markov Transforms
We express the generalized Cauchy-Stieltjes transforms of some particular Beta distributions depending on a positive parameter λ as λ-powered Cauchy-Stieltjes transforms of some probability measures. The Cauchy-Stieltjes transforms of the latter measures are shown to be the geometric mean of the Cauchy-Stieltjes transform of the Wigner law together with another one. Moreover, they are absolutel...
متن کاملSelf-adjointness of Cauchy Singular Integral Operator
We extend Krupnik’s criterion of self-adjointness of the Cauchy singular integral operator to the case of finitely connected domains. The main aim of the paper is to present a new approach for proof of the criterion. Let G+ be a finitely connected domain bounded by the rectifiable curve C = ∂G+, G− = C \ clos G+ and ∞ ∈ G−. Suppose also that w(z), z ∈ C is a nonnegative weight such that w(z) 6≡...
متن کاملar X iv : 0 70 5 . 01 68 v 2 [ m at h . PR ] 9 M ay 2 00 7 BROWNIAN SUBORDINATORS AND FRACTIONAL CAUCHY PROBLEMS
A Brownian time process is a Markov process subordinated to the absolute value of an independent one-dimensional Brownian motion. Its transition densities solve an initial value problem involving the square of the generator of the original Markov process. An apparently unrelated class of processes, emerging as the scaling limits of continuous time random walks, involve subordination to the inve...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015