Dirichlet Integrals on Harmonic Spaces
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803 Fumi-Yu ki Maeda
Dirichlet Integrals on Harmonic Spaces
Springer-Verlag Berlin Heidelberg New York 1980
Author Fumi-Yuki Maeda Dept. of Mathematics, Faculty of Science Hiroshima University Hiroshima, 730/Japan
AMS Subject Classifications (1980): 31 D 05 ISBN 3-540-09995-6 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-38?-09995-6 Springer-Verlag NewYork Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1980 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
ACKNOWLEDGEMENTS
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CONTENTS Introduction Terminology
Part §i.
§2.
§3.
Part §4.
I
................................................................... and notation
Theory Harmonic
........................................................
on G e n e r a l
Harmonic
spaces
i-i.
Definition Brelot's
1-3.
Bauer-Boboc-Constantinescu-Cornea's
1-4.
Examples
1-5.
Properties
of the b a s e
1-6.
Properties
of h y p e r h a r m o n i c
of h a r m o n i c
harmonic
spaces
space
.........................................
i
...............................................
3
harmonic
space
....................
..............................................................
Superharmonic
functions
2-1.
Superharmonic
2-2.
Potentials
2-3.
Reduced
2-4.
P-sets
2-5.
The
space
of a h a r m o n i c functions
space
.....................
................................
functions
..............................................
...........................................................
functions
....................................................
...............................................................
spaceR(U)
6 9 ii 13
and potentials
.......................................................
16 18 20 22 28
measures
3-1.
Measure
3-2
Existence
3-3
Properties
of m e a s u r
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