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 Advanced Studies in Pure Mathematics 2006; 413 pp; hardcover Volume: 44 ISBN-10: 4-931469-33-7 ISBN-13: 978-4-931469-33-4 List Price: US$104 Member Price: US$83.20 Order Code: ASPM/44 This volume collects, in written form, eight plenary lectures and twenty-five selected contributions from invited and contributed lectures delivered at the International Workshop on Potential Theory 2004. The workshop was held at Shimane University, Matsue, Japan, from August 23 to 28, 2004. The topic of the workshop was potential theory and its related fields. There were stimulus talks from classical potential theory to pluripotential theory and probabilistic potential theory. Volumes in this series are freely available electronically 5 years post-publication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership Graduate students and research mathematicians interested in analysis. Table of Contents Z. Błocki -- The Bergman kernel and pluripotential theory K. Burdzy -- Neumann eigenfunctions and Brownian couplings T. Carroll -- Brownian motion and harmonic measure in conic sections S. J. Gardiner -- Radial limits of harmonic functions Y. Guivarc'h -- Renewal theorems, products oif random matrices, and toral endomorphisms J. Ortega-Cerdà -- Densities and harmonic measure N. Shanmugalingam -- Sobolev type spaces on metric measure spaces J.-M. Wu -- Quasisymmetric extension, smoothing and applications J. Björn -- Wiener criterion for Cheeger $$p$$-harmonic functions on metric spaces F. Di Biase -- On the sharpness of certain approach regions T. Futamura and Y. Mizuta -- Continuity of weakly monotone Sobolev functions of variable exponent K. Hirata -- Martin kernels of general domains K. Ishizaki and N. Yanagihara -- Singular directions of meromorphic solutions of some non-autonomous Schröder equations K. Janssen -- Integral representation for space-time excessive functions T. Kurokawa -- A decomposition of the Schwartz class by a derivative space and its complementary space K. Kuwae and M. Takahashi -- Kato class functions of Markov processes under ultracontractivity E. G. Kwon -- A subharmonic Hardy class and Bloch pullback operator norms H. Masaoka -- Quasiconformal mappings and minimal Martin boundary of $$p$$-sheeted unlimited covering surfaces of the once punctered Riemann sphere $$\hat{\mathbb{C}}\setminus\{0\}$$ of Heins type H. Masaoka and S. Segawa -- Hyperbolic Riemann surfaces without unbounded positive harmonic functions I. Miyamoto and H. Yosida -- On a covering property of rarefied sets at infinity in a cone Y. Miyazaki -- The $$L^p$$ resolvents for elliptic systems of divergence form Y. Mizuta and T. Shimomura -- Maximal functions, Riesz potentials and Sobolev's inequality in generalized Lebesgue spaces M. Murata -- Representations of nonnegative solutions for parabolic equations M. Nakai -- Types of pasting arcs in two sheeted spheres M. Nishio, K. Shimomura, and N. Suzuki -- $$L^p$$-boundedness of Bergman projections for $$\alpha$$-parabolic operators Y. Okuyama -- Vanishing theorem on the pointwise defect of a rational iteration sequence for moving targets T. Ono -- Hölder continuity of solutions to quasilinear elliptic equations with measure data Y. Pinchover -- On Davies' conjecture and strong ratio limit properties for the heat kernel Premaltha and A. K. Kalyani -- Some potential theoretic results of an infinite network M. Stoll -- The Littlewood-Paley inequalities for Hardy-Orlicz spaces of harmonic functions on domains in $$\mathbb{R}^n$$ H. Watanabe -- Estimates of maximal functions by Hausdorff contents in a metric space M. Yamada -- Harmonic conjugates of parabolic Bergman functions M. Yanagishita -- On the behavior at infinity for non-negative superharmonic functions in a cone