scholarly journals $\varepsilon $-approximability of harmonic functions in $L^p$ implies uniform rectifiability

2019 ◽  
Vol 147 (5) ◽  
pp. 2107-2121
Author(s):  
Simon Bortz ◽  
Olli Tapiola
Keyword(s):  
Harmonic Functions ◽  
Uniform Rectifiability

scholarly journals Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions

2016 ◽  
Vol 165 (12) ◽  
pp. 2331-2389 ◽  
Author(s):  
Steve Hofmann ◽  
José María Martell ◽  
Svitlana Mayboroda
Keyword(s):  
Harmonic Functions ◽  
Carleson Measure ◽  
Uniform Rectifiability

On the Radial Symmetry Property for Harmonic Functions

2020 ◽  
Vol 64 (10) ◽  
pp. 9-19
Author(s):  
V. V. Volchkov ◽  
Vit. V. Volchkov
Keyword(s):  
Harmonic Functions ◽  
Symmetry Property ◽  
Radial Symmetry

Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle

2005 ◽  
Vol 11 (4) ◽  
pp. 517-525
Author(s):  
Juris Steprāns
Keyword(s):  
Harmonic Analysis ◽  
Set Theory ◽  
Harmonic Functions ◽  
Maximal Functions ◽  
Pigeonhole Principle ◽  
Cardinal Invariants ◽  
Geometric Objects

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

scholarly journals On the existence of various bounded harmonic functions with given periods, II

1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara
Keyword(s):  
Riemann Surface ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Dirichlet Integral ◽  
Period Function ◽  
Boundedness Property ◽  
One Dimensional ◽  
Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

scholarly journals Uniform Rectifiability and Elliptic Operators Satisfying a Carleson Measure Condition

2021 ◽  
Author(s):  
Steve Hofmann ◽  
José María Martell ◽  
Svitlana Mayboroda ◽  
Tatiana Toro ◽  
Zihui Zhao
Keyword(s):  
Carleson Measure ◽  
Elliptic Operators ◽  
Uniform Rectifiability
Sign in / Sign up

Export Citation Format

Share Document