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math.FA2015
Hardy-Stein identities and square functions for semigroups
Rodrigo Bañuelos, Krzysztof Bogdan, Tomasz Luks
We prove a Hardy-Stein type identity for the semigroups of symmetric, pure-jump Lévy processes. Combined with the Burkholder-Gundy inequalities, it gives the two-way boundedn…
math.FA2011
Boundary behavior of α-harmonic functions on the complement of the sphere and hyperplane
Tomasz Luks
We study α-harmonic functions on the complement of the sphere and on the complement of the hyperplane in Euclidean spaces of dimension bigger than one, for α\in(1,2). We describe t…
math.FA2011
On Hardy spaces of local and nonlocal operators
Krzysztof Bogdan, Bartłomiej Dyda, Tomasz Luks
We characterize conditional Hardy spaces of the Laplacian and of the fractional Laplacian by using Hardy-Stein type identities.