Differentiable Lp-functional calculus for certain sums of non-commuting operators
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Submission date: 06. Sep. 2005 (revised version: September 2005)
published in: Colloquium mathematicum, 105 (2006) 1, p. 105-125
DOI number (of the published article): 10.4064/cm105-1-10
MSC-Numbers: 47A60, 47B25, 22E25, 22E30
Keywords and phrases: spectral multiplier, functional calculus, solvable lie groups
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We consider a special class of sums of non-commuting positive operators on -spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable -functional calculus for . Our results are in particular applicable to certain sub-Laplacians, Schrödinger operators and sums of even powers of vector fields on solvable Lie groups with exponential volume growth.