# CAPACITY

The ${\cal C}^{1}\text{-harmonic}$ capacity κ c plays a central role in problems of approximation by harmonic functions in the ${\cal C}^{1}\text{-norm}$ in ${\Bbb R}^{n+1}$ . In this paper we prove the comparability between the capacity κ c and its positive version $\kappa _{+}^{c}$ . As a... Full description

1st Person: DE VILLA, ALEIX RUIZ TOLSA, XAVIER in Transactions of the American Mathematical Society Vol. 362, No. 7 (2010), p. 3641-3675 More Articles Article English 2010 Volltext
LEADER 001 003 01504nma a2200301 c 4500 JST104141999 DE-601 20180527151229.0 cr uuu---uuuuu 180527s2010 000 0 eng d 8 |a 25677842 |a 25677842 |b ger  |c GBVCP 0 |a eng 1 |a DE VILLA, ALEIX RUIZ 1 0 |a CAPACITY  |h Elektronische Ressource |a Online-Ressource |a Copyright: © 2010 American Mathematical Society |a The ${\cal C}^{1}\text{-harmonic}$ capacity κ c plays a central role in problems of approximation by harmonic functions in the ${\cal C}^{1}\text{-norm}$ in ${\Bbb R}^{n+1}$ . In this paper we prove the comparability between the capacity κ c and its positive version $\kappa _{+}^{c}$ . As a corollary, we deduce the semiadditivity of κ c . This capacity can be considered as a generalization in ${\Bbb R}^{n+1}$ of the continuous analytic capacity α in ${\Bbb C}$ . Moreover, we also show that the so-called inner boundary conjecture fails for dimensions n > 1, unlike in the case n = 1. 2 7 |a research-article  |2 gnd 0 0 |A f  |a research-article 0 |5 DE-601 1 |a TOLSA, XAVIER 0 8 |i in  |t Transactions of the American Mathematical Society  |g Vol. 362, No. 7 (2010), p. 3641-3675  |q 362:7<3641-3675  |w (DE-601)JST086523945  |x 0002-9947 4 1 |u https://www.jstor.org/stable/25677842  |3 Volltext |a GBV_JSTOR |a AR |d 362  |j 2010  |e 7  |h 3641-3675

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