Stable Lévy processes and related stochastic processes play an important role in stochastic
modelling in applied sciences, in particular in financial mathematics. This book is about the …

Differential forms have been widely studied and used in many fields, such as physics,
general relativity, theory of elasticity, quasiconformal analysis, electromagnetism, and …

arXiv:0807.1825v1 [math.AP] 11 Jul 2008 Page 1 arXiv:0807.1825v1 [math.AP] 11 Jul 2008
THE BEST CONSTANT IN A FRACTIONAL HARDY INEQUALITY KRZYSZTOF BOGDAN AND …

We prove a uniform boundary Harnack inequality for nonnegative harmonic functions of the
fractional Laplacian on arbitrary open set D. This yields a unique representation of such …

We prove that in the Euclidean space of arbitrary dimension the inversion of the isotropic
stable Lévy process killed at the origin is, after an appropriate change of time, the same …

We prove that bounded harmonic functions of anisotropic fractional Laplacians are Hölder
continuous under mild regularity assumptions on the corresponding Lévy measure. Under …

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On Hardy spaces of local and nonlocal operators Page 1 Hiroshima Math. J. 44 (2014), 193–215
On Hardy spaces of local and nonlocal operators Krzysztof Bogdan, Bartłomiej Dyda and …

Abstract For any α∈(0, 2), a truncated symmetric α-stable process in ℝ d is a symmetric Lévy
process in ℝ d with no diffusion part and with a Lévy density given by c| x|− d− α 1 {| x|< 1} for …

Recently it was shown in [P. Kim, Fatou's theorem for censored stable processes, Stochastic
Process. Appl. 108 (1)(2003) 63–92] that Fatou's theorem for transient censored α-stable …