International Workshop on Potential Theory 2004
August 23–28, 2004 | Shimane University, Matsue, Japan
Potential Theory in Matsue

Editor(s) Hiroaki Aikawa, Takashi Kumagai, Yoshihiro Mizuta, Noriaki Suzuki

Adv. Stud. Pure Math., 44: 413pp. (2006). DOI: 10.2969/aspm/04410000
TABLE OF CONTENTS
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Advanced Studies in Pure Mathematics Vol. 44, - (2006).
Hiroaki Aikawa , Takashi Kumagai , Yoshihiro Mizuta , Noriaki Suzuki
Advanced Studies in Pure Mathematics Vol. 44, - (2006).
Advanced Studies in Pure Mathematics Vol. 44, - (2006).
Advanced Studies in Pure Mathematics Vol. 44, - (2006).
Zbigniew Błocki
Advanced Studies in Pure Mathematics Vol. 44, 1-9 (2006). https://doi.org/10.2969/aspm/04410001
KEYWORDS: Bergman kernel, Bergman metric, pluricomplex Green function, hyperconvex domains, 32A25, 32U15
Krzysztof Burdzy
Advanced Studies in Pure Mathematics Vol. 44, 11-23 (2006). https://doi.org/10.2969/aspm/04410011
KEYWORDS: 35J05, 60J65, 35P05, 60H30
Tom Carroll
Advanced Studies in Pure Mathematics Vol. 44, 25-41 (2006). https://doi.org/10.2969/aspm/04410025
KEYWORDS: Brownian motion, harmonic measure, conformal mapping, 60J65, 30C35, 30C85, 31A15
Stephen J. Gardiner
Advanced Studies in Pure Mathematics Vol. 44, 43-51 (2006). https://doi.org/10.2969/aspm/04410043
KEYWORDS: 31B05
Yves Guivarc'h
Advanced Studies in Pure Mathematics Vol. 44, 53-66 (2006). https://doi.org/10.2969/aspm/04410053
Joaquim Ortega-Cerdà
Advanced Studies in Pure Mathematics Vol. 44, 67-76 (2006). https://doi.org/10.2969/aspm/04410067
KEYWORDS: harmonic measure, densities, sampling sequences, interpolating sequences, zero sequences, 31, 32
Nageswari Shanmugalingam
Advanced Studies in Pure Mathematics Vol. 44, 77-90 (2006). https://doi.org/10.2969/aspm/04410077
KEYWORDS: Newtonian space, upper gradients, metric measure spaces, Poincaré inequality, 31C45
Jang-Mei Wu
Advanced Studies in Pure Mathematics Vol. 44, 91-101 (2006). https://doi.org/10.2969/aspm/04410091
KEYWORDS: branch sets, quasiregular maps, quasiconformal dimensions, 30C65, 28A78
Jana Björn
Advanced Studies in Pure Mathematics Vol. 44, 103-115 (2006). https://doi.org/10.2969/aspm/04410103
KEYWORDS: boundary regularity, capacity, Cheeger $p$-harmonic, doubling metric measure space, Poincaré inequality, pointwise estimate, Wiener criterion, 31C45, 31C15, 35J65, 35J60
Fausto Di Biase
Advanced Studies in Pure Mathematics Vol. 44, 117-125 (2006). https://doi.org/10.2969/aspm/04410117
KEYWORDS: Harmonic functions, inner functions, boundary behaviour, almost everywhere convergence, Lebesgue points, tangential approach, sharp approach regions, independence proofs, unit disc, nontangentially accessible domains, pseudoconvex domains, holomorphic functions, 31A20, 03E15, 31B25, 32A40
Toshihide Futamura , Yoshihiro Mizuta
Advanced Studies in Pure Mathematics Vol. 44, 127-143 (2006). https://doi.org/10.2969/aspm/04410127
KEYWORDS: weakly monotone Sobolev functions of variable exponent, 0-Hölder continuous, capacity, tangential boundary limits, 30C65, 31B15, 46E35
Kentaro Hirata
Advanced Studies in Pure Mathematics Vol. 44, 145-154 (2006). https://doi.org/10.2969/aspm/04410145
KEYWORDS: Martin kernel, boundary behavior, comparison estimate, John domain, uniform domain, 31C35, 31B05, 31B25
Katsuya Ishizaki , Niro Yanagihara
Advanced Studies in Pure Mathematics Vol. 44, 155-166 (2006). https://doi.org/10.2969/aspm/04410155
KEYWORDS: Schröder equation, Nevanlinna theory, Borel direction Value distribution theory in angular domains, 30D35, 39B32
Klaus Janssen
Advanced Studies in Pure Mathematics Vol. 44, 167-177 (2006). https://doi.org/10.2969/aspm/04410167
Takahide Kurokawa
Advanced Studies in Pure Mathematics Vol. 44, 179-191 (2006). https://doi.org/10.2969/aspm/04410179
KEYWORDS: Schwartz class, derivative space, complementary space, 46E10
Kazuhiro Kuwae , Masayuki Takahashi
Advanced Studies in Pure Mathematics Vol. 44, 193-202 (2006). https://doi.org/10.2969/aspm/04410193
KEYWORDS: Dirichlet form, Markov process, Kato class, Dynkin class, heat kernel, semigroup kernel, resolvent kernel, Green kernel, ultracontractivity, Nash type inequality, Sobolev inequality, Brownian motion, symmetric $\alpha$-stable process, relativistic Hamiltonian process, Brownian motion penetrating fractals, 31-XX, 31C15, 31C25, 60G52, 60Jxx, 60J25, 60J45, 60J60, 60J65, 60J75
Ern Gun Kwon
Advanced Studies in Pure Mathematics Vol. 44, 203-210 (2006). https://doi.org/10.2969/aspm/04410203
KEYWORDS: 30D05, 30D45, 30D50, 30D55
Hiroaki Masaoka
Advanced Studies in Pure Mathematics Vol. 44, 211-226 (2006). https://doi.org/10.2969/aspm/04410211
KEYWORDS: Martin boundary, covering surface, quasiconformal mappings, 31C35, 30F25
Hiroaki Masaoka , Shigeo Segawa
Advanced Studies in Pure Mathematics Vol. 44, 227-232 (2006). https://doi.org/10.2969/aspm/04410227
KEYWORDS: hyperbolic Riemann surface, positive harmonic function, Martin boundary, harmonic measure, 30F15, 30F20, 30F25, 31C35
Ikuko Miyamoto , Hidenobu Yosida
Advanced Studies in Pure Mathematics Vol. 44, 233-244 (2006). https://doi.org/10.2969/aspm/04410233
KEYWORDS: rarefied set, cone, 31B05
Yoichi Miyazaki
Advanced Studies in Pure Mathematics Vol. 44, 245-254 (2006). https://doi.org/10.2969/aspm/04410245
KEYWORDS: elliptic system, $L^p$ theory, non-smooth coefficients, heat kernel, resolvent kernel, 35G05, 35B20, 31B10
Yoshihiro Mizuta , Tetsu Shimomura
Advanced Studies in Pure Mathematics Vol. 44, 255-281 (2006). https://doi.org/10.2969/aspm/04410255
KEYWORDS: Lebesgue spaces with variable exponent, maximal functions, Riesz potentials, Sobolev's inequality, Hardy's inequality, 42B25, 46E30, 31B15
Minoru Murata
Advanced Studies in Pure Mathematics Vol. 44, 283-289 (2006). https://doi.org/10.2969/aspm/04410283
KEYWORDS: parabolic equation, nonnegative solution, integral representation, Martin boundary, intrinsic ultracontractivity, semismall perturbation, 31C35, 35C15, 31C12, 35J99, 35K15, 35K99, 58J99
Mitsuru Nakai
Advanced Studies in Pure Mathematics Vol. 44, 291-304 (2006). https://doi.org/10.2969/aspm/04410291
KEYWORDS: capacity, covering surface, Dirichlet integral, Dirichlet principle, harmonic measure, modulus, two sheeted plane (sphere), 31A15, 31C15, 30C85, 30F15
Masaharu Nishio , Katsunori Shimomura , Noriaki Suzuki
Advanced Studies in Pure Mathematics Vol. 44, 305-318 (2006). https://doi.org/10.2969/aspm/04410305
KEYWORDS: parabolic operator of fractional order, Bergman space, Bergman projection, Huygens property, reproducing kernel, 31B10, 35K05, 46E15
Yûsuke Okuyama
Advanced Studies in Pure Mathematics Vol. 44, 319-325 (2006). https://doi.org/10.2969/aspm/04410319
KEYWORDS: pointwise proximity function, Valiron defect, moving target, complex dynamics, 30D05, 39B32, 37F10
Takayori Ono
Advanced Studies in Pure Mathematics Vol. 44, 327-338 (2006). https://doi.org/10.2969/aspm/04410327
KEYWORDS: quasi-linear equation with measure data, Hölder continuity, 31C45, 31B25
Yehuda Pinchover
Advanced Studies in Pure Mathematics Vol. 44, 339-352 (2006). https://doi.org/10.2969/aspm/04410339
KEYWORDS: heat kernel, ratio limit theorem, recurrence, 35K10, 35B40, 58J35, 60J60
A. K. Kalyani
Advanced Studies in Pure Mathematics Vol. 44, 353-362 (2006). https://doi.org/10.2969/aspm/04410353
KEYWORDS: Hyperbolic network, greatest harmonic minorant, potential, Poisson integral, reduced function, 31C20
Manfred Stoll
Advanced Studies in Pure Mathematics Vol. 44, 363-376 (2006). https://doi.org/10.2969/aspm/04410363
KEYWORDS: Green's function, Hardy-Orlicz spaces, harmonic function, harmonic majorant, holomorphic function, subharmonic function, 30D55, 31B05
Hisako Watanabe
Advanced Studies in Pure Mathematics Vol. 44, 377-389 (2006). https://doi.org/10.2969/aspm/04410377
KEYWORDS: maximal function, Hausdorff content, homogeneous space, Choquet integral, 31B15, 42B25
Masahiro Yamada
Advanced Studies in Pure Mathematics Vol. 44, 391-402 (2006). https://doi.org/10.2969/aspm/04410391
KEYWORDS: Bergman space, harmonic conjugate, heat equation, parabolic equation, 32A36, 26D10, 35K05
Minoru Yanagishita
Advanced Studies in Pure Mathematics Vol. 44, 403-413 (2006). https://doi.org/10.2969/aspm/04410403
KEYWORDS: cone, superharmonic functions, $\alpha$-minimally thin sets, 31B05, 31B20
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