AbstractThe aim of this article is to provide a functional analytical framework for defining the fractional powers{A^{s}} for {-1<s<1} of maximal monotone (possibly multivalued and nonlinear) operators A in Hilbert spaces.
We investigate the semigroup {\{e^{-A^{s}t}\}_{t\geq 0}} generated by {-A^{s}}, prove comparison principles and interpolations properties of {\{e^{-A^{s}t}\}_{t\geq 0}} in Lebesgue and Orlicz spaces.
We give sufficient conditions implying that {A^{s}} has a sub-differential structure.
These results extend earlier ones obtained in the case {s=1/2} for maximal monotone operators
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An Extension Problem and Trace Hardy Inequality for the Sub-Laplacian on H-type Groups