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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The equivalence of two definitions of capacity


Authors: David R. Adams and John C. Polking
Journal: Proc. Amer. Math. Soc. 37 (1973), 529-534
MSC: Primary 31B15
DOI: https://doi.org/10.1090/S0002-9939-1973-0328109-5
MathSciNet review: 0328109
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Abstract: It is shown that two definitions for an ${L_p}$ capacity $(1 < p < \infty )$ on subsets of Euclidean ${R^n}$ are equivalent in the sense that as set functions their ratio is bounded above and below by positive finite constants. The classical notions of capacity correspond to the case $p = 2$.


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Keywords: Capacity, Bessel potentials of <IMG WIDTH="29" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${L_p}$"> functions, fractional differentiation operators, functions that operate
Article copyright: © Copyright 1973 American Mathematical Society