Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Integral geometric properties of capacities
HTML articles powered by AMS MathViewer

by Pertti Mattila PDF
Trans. Amer. Math. Soc. 266 (1981), 539-554 Request permission

Abstract:

Let $m$ and $n$ be positive integers, $0 < m < n$, and ${C_K}$ and ${C_H}$ the usual potential-theoretic capacities on ${R^n}$ corresponding to lower semicontinuous kernels $K$ and $H$ on ${R^n} \times {R^n}$ with $H(x,y) = K(x,y){\left | {x - y} \right |^{n - m}} \geqslant 1$ for $\left | {x - y} \right | \leqslant 1$. We consider relations between the capacities ${C_K}(E)$ and ${C_H}(E \cap A)$ when $E \subset {R^n}$ and $A$ varies over the $m$-dimensional affine subspaces of ${R^n}$. For example, we prove that if $E$ is compact, ${C_K}(E) \leqslant c\smallint {C_H}(E \cap A)d{\lambda _{n,m}}A$ where ${\lambda _{n,m}}$ is a rigidly invariant measure and $c$ is a positive constant depending only on $n$ and $m$.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 31B15, 28A75, 31C15
  • Retrieve articles in all journals with MSC: 31B15, 28A75, 31C15
Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 266 (1981), 539-554
  • MSC: Primary 31B15; Secondary 28A75, 31C15
  • DOI: https://doi.org/10.1090/S0002-9947-1981-0617550-8
  • MathSciNet review: 617550