TY - JOUR
T1 - Characterization and semiadditivity of the c1-harmonic capacity
AU - De Villa, Aleix Ruiz
AU - Tolsa, Xavier
PY - 2010/7/1
Y1 - 2010/7/1
N2 - The C1-harmonic capacity ?c plays a central role in problems of approximation by harmonic functions in the C1-norm in ℝn+1. In this paper we prove the comparability between the capacity ?c and its positive version ?c+ . As a corollary, we deduce the semiadditivity of ?c. This capacity can be considered as a generalization in ℝn+1 of the continuous analytic capacity α in ℂ. Moreover, we also show that the so-called inner boundary conjecture fails for dimensions n > 1, unlike in the case n = 1. © 2010 American Mathematical Society.
AB - The C1-harmonic capacity ?c plays a central role in problems of approximation by harmonic functions in the C1-norm in ℝn+1. In this paper we prove the comparability between the capacity ?c and its positive version ?c+ . As a corollary, we deduce the semiadditivity of ?c. This capacity can be considered as a generalization in ℝn+1 of the continuous analytic capacity α in ℂ. Moreover, we also show that the so-called inner boundary conjecture fails for dimensions n > 1, unlike in the case n = 1. © 2010 American Mathematical Society.
U2 - 10.1090/S0002-9947-10-05105-6
DO - 10.1090/S0002-9947-10-05105-6
M3 - Article
SN - 0002-9947
VL - 362
SP - 3641
EP - 3675
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 7
ER -